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Adelhardt P, Koziol JA, Langheld A, Schmidt KP. Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. ENTROPY (BASEL, SWITZERLAND) 2024; 26:401. [PMID: 38785650 PMCID: PMC11120707 DOI: 10.3390/e26050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Revised: 04/17/2024] [Accepted: 04/19/2024] [Indexed: 05/25/2024]
Abstract
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.
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Affiliation(s)
| | | | | | - Kai P. Schmidt
- Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany; (P.A.); (J.A.K.); (A.L.)
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2
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Chakraborty N, Heyl M, Karpov P, Moessner R. Spectral Response of Disorder-Free Localized Lattice Gauge Theories. PHYSICAL REVIEW LETTERS 2023; 131:220402. [PMID: 38101388 DOI: 10.1103/physrevlett.131.220402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Accepted: 10/31/2023] [Indexed: 12/17/2023]
Abstract
We show that certain lattice gauge theories exhibiting disorder-free localization have a characteristic response in spatially averaged spectral functions: a few sharp peaks combined with vanishing response in the zero frequency limit. This reflects the discrete spectra of small clusters of kinetically active regions formed in such gauge theories when they fragment into spatially finite clusters in the localized phase due to the presence of static charges. We obtain the transverse component of the dynamic structure factor, which is probed by neutron scattering experiments, deep in this phase from a combination of analytical estimates and a numerical cluster expansion. We also show that local spectral functions of large finite clusters host discrete peaks whose positions agree with our analytical estimates. Further, information spreading, diagnosed by an unequal time commutator, halts due to real space fragmentation. Our results can be used to distinguish the disorder-free localized phase from conventional paramagnetic counterparts in those frustrated magnets which might realize such an emergent gauge theory.
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Affiliation(s)
- Nilotpal Chakraborty
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, Dresden 01187, Germany
| | - Markus Heyl
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, Dresden 01187, Germany
- Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany
| | - Petr Karpov
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, Dresden 01187, Germany
| | - Roderich Moessner
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, Dresden 01187, Germany
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3
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Mao D, Zhang K, Kim EA. Fractionalization in Fractional Correlated Insulating States at n±1/3 Filled Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:106801. [PMID: 37739384 DOI: 10.1103/physrevlett.131.106801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Revised: 07/13/2023] [Accepted: 08/17/2023] [Indexed: 09/24/2023]
Abstract
Fractionalization without time-reversal symmetry breaking is a long-sought-after goal in the study of correlated phenomena. The earlier proposal of correlated insulating states at n±1/3 filling in twisted bilayer graphene and recent experimental observations of insulating states at those fillings strongly suggest that moiré graphene systems provide a new platform to realize time-reversal symmetric fractionalized states. However, the nature of fractional excitations and the effect of quantum fluctuation on the fractional correlated insulating states are unknown. We show that excitations of the fractional correlated insulator phases in the strong coupling limit carry fractional charges and exhibit fractonic restricted mobility. Upon introduction of quantum fluctuations, the resonance of "lemniscate" structured operators drives the system into quantum lemniscate liquid (QLL) or quantum lemniscate solid (QLS). We find an emergent U(1)×U(1) 1-form symmetry unifies distinct motions of the fractionally charged excitations in the strong coupling limit and in the QLL phase, while providing a new mechanism for fractional excitations in two dimensions. We predict emergent Luttinger liquid behavior upon dilute doping in the strong coupling limit due to restricted mobility and discuss implications at a general n±1/3 filling.
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Affiliation(s)
- Dan Mao
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
| | - Kevin Zhang
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
| | - Eun-Ah Kim
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
- Radcliffe Institute for Advanced Study at Harvard, Harvard University, 10 Garden Street, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
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4
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Han Z, Kivelson SA. Resonating Valence Bond States in an Electron-Phonon System. PHYSICAL REVIEW LETTERS 2023; 130:186404. [PMID: 37204902 DOI: 10.1103/physrevlett.130.186404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 04/14/2023] [Indexed: 05/21/2023]
Abstract
We study a simple electron-phonon model on square and triangular versions of the Lieb lattice using an asymptotically exact strong coupling analysis. At zero temperature and electron density n=1 (one electron per unit cell), for various ranges of parameters in the model, we exploit a mapping to the quantum dimer model to establish the existence of a spin-liquid phase with Z_{2} topological order (on the triangular lattice) and a multicritical line corresponding to a quantum critical spin liquid (on the square lattice). In the remaining part of the phase diagram, we find a host of charge-density-wave phases (valence-bond solids), a conventional s-wave superconducting phase, and with the addition of a small Hubbard U to tip the balance, a phonon-induced d-wave superconducting phase. Under a special condition, we find a hidden pseudospin SU(2) symmetry that implies an exact constraint on the superconducting order parameters.
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Affiliation(s)
- Zhaoyu Han
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Steven A Kivelson
- Department of Physics, Stanford University, Stanford, California 94305, USA
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5
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Samajdar R, Joshi DG, Teng Y, Sachdev S. Emergent Z_{2} Gauge Theories and Topological Excitations in Rydberg Atom Arrays. PHYSICAL REVIEW LETTERS 2023; 130:043601. [PMID: 36763444 DOI: 10.1103/physrevlett.130.043601] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 12/05/2022] [Indexed: 06/18/2023]
Abstract
Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z_{2} gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological Z_{2} quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also discuss the natures of the fractionalized excitations of these Z_{2} spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.
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Affiliation(s)
- Rhine Samajdar
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, Princeton University, Princeton, New Jersey, 08544, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey, 08544, USA
| | - Darshan G Joshi
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Yanting Teng
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA
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6
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Triangular lattice quantum dimer model with variable dimer density. Nat Commun 2022; 13:5799. [PMID: 36184678 PMCID: PMC9527248 DOI: 10.1038/s41467-022-33431-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 09/15/2022] [Indexed: 12/02/2022] Open
Abstract
Quantum dimer models are known to host topological quantum spin liquid phases, and it has recently become possible to simulate such models with Rydberg atoms trapped in arrays of optical tweezers. Here, we present large-scale quantum Monte Carlo simulation results on an extension of the triangular lattice quantum dimer model with terms in the Hamiltonian annihilating and creating single dimers. We find distinct odd and even \documentclass[12pt]{minimal}
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\begin{document}$${{\mathbb{Z}}}_{2}$$\end{document}Z2 spin liquids, along with several phases with no topological order: a staggered crystal, a nematic phase, and a trivial symmetric phase with no obvious broken symmetry. We also present dynamic spectra of the phases, and note implications for experiments on Rydberg atoms. Quantum dimer models are known to host topological quantum spin liquid phases, and it has recently become possible to simulate related \documentclass[12pt]{minimal}
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\begin{document}$${{\mathbb{Z}}}_{2}$$\end{document}Z2 gauge theories with Rydberg atoms. Yan et al. compute the phase diagram of an experimentally motivated quantum dimer model on a triangular lattice with fluctuating dimer density.
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Multiple strongly coupled antiferromagnetic spin S = 1/2 dimers in liroconite Cu 2Al(As,P)O 4(OH) 4·4H 2O. Z KRIST-CRYST MATER 2022. [DOI: 10.1515/zkri-2022-0040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
We report on the magneto-structural properties of the rare copper aluminum hydroxo-arsenate mineral liroconite with chemical composition Cu2AlAs1−x
P
x
O4(OH)4·4H2O (x ≈ 0.2). In order to characterize the natural mineral sample chemical analyses, X-ray single crystal and powder diffraction, heat capacity and crystal water desorption, anisotropic thermal expansion and Raman scattering and magnetic susceptibility investigations have been carried out. The magnetic properties are well described by two discrete oxygen bridged Cu2+ spin S = 1/2 dimers with antiferromagnetic spin exchange ranging between −320 K and −136 K, depending on to which group-15 five-valent cation, As5+ or P5+, the dimer bridging oxygen atoms coordinate to. Accordingly the temperature dependence of the magnetic susceptibilities can be well fitted to a sum of two Bleaney–Bowers type spin S = 1/2 dimer susceptibilities suggesting that the dimers show negligible mixed coordination to (AsO4)3−/(PO4)3− tetrahedra. DFT + U calculation confirm the ratio of the spin exchange parameters of the (AsO4)3− or (PO4)3− coordinated Cu2+ – Cu2+ dimers. Inter dimer spin exchange is about two orders of magnitude smaller than intra dimer exchange.
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8
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Giudici G, Lukin MD, Pichler H. Dynamical Preparation of Quantum Spin Liquids in Rydberg Atom Arrays. PHYSICAL REVIEW LETTERS 2022; 129:090401. [PMID: 36083676 DOI: 10.1103/physrevlett.129.090401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Accepted: 08/03/2022] [Indexed: 06/15/2023]
Abstract
We theoretically analyze recent experiments [Semeghini et al., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase-the resonating valence bond state of hard dimers-in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.
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Affiliation(s)
- Giuliano Giudici
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 München, Germany
- Arnold Sommerfeld Center for Theoretical Physics, University of Munich, Theresienstraße 37, 80333 München, Germany
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Hannes Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
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9
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Rose DC, Macieszczak K, Lesanovsky I, Garrahan JP. Hierarchical classical metastability in an open quantum East model. Phys Rev E 2022; 105:044121. [PMID: 35590670 DOI: 10.1103/physreve.105.044121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Accepted: 03/18/2022] [Indexed: 06/15/2023]
Abstract
We study in detail an open quantum generalization of a classical kinetically constrained model-the East model-known to exhibit slow glassy dynamics stemming from a complex hierarchy of metastable states with distinct lifetimes. Using the recently introduced theory of classical metastability for open quantum systems, we show that the driven open quantum East model features a hierarchy of classical metastabilities at low temperature and weak driving field. We find that the effective long-time description of its dynamics not only is classical, but shares many properties with the classical East model, such as obeying an effective detailed balance condition and lacking static interactions between excitations, but with this occurring within a modified set of metastable phases which are coherent, and with an effective temperature that is dependent on the coherent drive.
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Affiliation(s)
- Dominic C Rose
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Katarzyna Macieszczak
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Ave., Cambridge CB3 0HE, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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10
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Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers. Symmetry (Basel) 2022. [DOI: 10.3390/sym14030624] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.
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11
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Myerson-Jain NE, Liu S, Ji W, Xu C, Vijay S. Pascal's Triangle Fractal Symmetries. PHYSICAL REVIEW LETTERS 2022; 128:115301. [PMID: 35363032 DOI: 10.1103/physrevlett.128.115301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Revised: 01/23/2022] [Accepted: 02/18/2022] [Indexed: 06/14/2023]
Abstract
We introduce a model of interacting bosons exhibiting an infinite collection of fractal symmetries-termed "Pascal's triangle symmetries"-which provides a natural U(1) generalization of a spin-(1/2) system with Sierpinski triangle fractal symmetries introduced in Newman et al., [Phys. Rev. E 60, 5068 (1999).PLEEE81063-651X10.1103/PhysRevE.60.5068]. The Pascal's triangle symmetry gives rise to exact degeneracies, as well as a manifold of low-energy states which are absent in the Sierpinski triangle model. Breaking the U(1) symmetry of this model to Z_{p}, with prime integer p, yields a lattice model with a unique fractal symmetry which is generated by an operator supported on a fractal subsystem with Hausdorff dimension d_{H}=ln(p(p+1)/2)/lnp. The Hausdorff dimension of the fractal can be probed through correlation functions at finite temperature. The phase diagram of these models at zero temperature in the presence of quantum fluctuations, as well as the potential physical construction of the U(1) model, is discussed.
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Affiliation(s)
- Nayan E Myerson-Jain
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Shang Liu
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Wenjie Ji
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Cenke Xu
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Sagar Vijay
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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12
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Wiese UJ. From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210068. [PMID: 34923839 DOI: 10.1098/rsta.2021.0068] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2021] [Accepted: 08/18/2021] [Indexed: 06/14/2023]
Abstract
Quantum link models provide an extension of Wilson's lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson's parallel transporters, quantum links are intrinsically quantum degrees of freedom. In D-theory, these discrete variables undergo dimensional reduction, thus giving rise to asymptotically free theories. In this way [Formula: see text] [Formula: see text] models emerge by dimensional reduction from [Formula: see text] [Formula: see text] quantum spin ladders, the [Formula: see text] confining [Formula: see text] gauge theory emerges from the Abelian Coulomb phase of a [Formula: see text] quantum link model, and [Formula: see text] QCD arises from a non-Abelian Coulomb phase of a [Formula: see text] [Formula: see text] quantum link model, with chiral quarks arising naturally as domain wall fermions. Thanks to their finite-dimensional Hilbert space and their economical mechanism of reaching the continuum limit by dimensional reduction, quantum link models provide a resource efficient framework for the quantum simulation and computation of gauge theories. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- Uwe-Jens Wiese
- Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
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13
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Gökmen DE, Ringel Z, Huber SD, Koch-Janusz M. Statistical Physics through the Lens of Real-Space Mutual Information. PHYSICAL REVIEW LETTERS 2021; 127:240603. [PMID: 34951810 DOI: 10.1103/physrevlett.127.240603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Revised: 08/10/2021] [Accepted: 10/13/2021] [Indexed: 06/14/2023]
Abstract
Identifying the relevant degrees of freedom in a complex physical system is a key stage in developing effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, lack formal interpretability. Here we present an algorithm employing state-of-the-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges, and use this advance to develop a new paradigm in identifying the most relevant operators describing properties of the system. We demonstrate this on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic constituents. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way toward automated theory building.
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Affiliation(s)
- Doruk Efe Gökmen
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Zohar Ringel
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Sebastian D Huber
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Maciej Koch-Janusz
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
- Department of Physics, University of Zurich, 8057 Zurich, Switzerland
- James Franck Institute, The University of Chicago, Chiccago, Illinois 60637, USA
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14
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Singh H, Ware BA, Vasseur R, Friedman AJ. Subdiffusion and Many-Body Quantum Chaos with Kinetic Constraints. PHYSICAL REVIEW LETTERS 2021; 127:230602. [PMID: 34936767 DOI: 10.1103/physrevlett.127.230602] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic timescales are given by the inverse gap of an effective Hamiltonian-or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, t_{Th}, determined by the spectral form factor, to transport properties and linear-response correlators. Using tensor network methods, we determine the dynamical exponent z for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with "Fredkin" constraints exhibit anomalous transport with dynamical exponent z≃8/3.
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Affiliation(s)
- Hansveer Singh
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Brayden A Ware
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Aaron J Friedman
- Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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15
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Semeghini G, Levine H, Keesling A, Ebadi S, Wang TT, Bluvstein D, Verresen R, Pichler H, Kalinowski M, Samajdar R, Omran A, Sachdev S, Vishwanath A, Greiner M, Vuletić V, Lukin MD. Probing topological spin liquids on a programmable quantum simulator. Science 2021; 374:1242-1247. [PMID: 34855494 DOI: 10.1126/science.abi8794] [Citation(s) in RCA: 77] [Impact Index Per Article: 25.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing, Boston, MA 02135, USA
| | - S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - R Verresen
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - M Kalinowski
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - R Samajdar
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing, Boston, MA 02135, USA
| | - S Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
| | - A Vishwanath
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - V Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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16
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Jiang YF, Yao H, Yang F. Possible Superconductivity with a Bogoliubov Fermi Surface in a Lightly Doped Kagome U(1) Spin Liquid. PHYSICAL REVIEW LETTERS 2021; 127:187003. [PMID: 34767423 DOI: 10.1103/physrevlett.127.187003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2020] [Revised: 05/22/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
Whether the doped t-J model on the Kagome lattice supports exotic superconductivity has not been decisively answered. In this Letter, we propose a new class of variational states for this model and perform a large-scale variational Monte Carlo simulation on it. The proposed variational states are parameterized by the SU(2)-gauge rotation angles, as the SU(2)-gauge structure hidden in the Gutzwiller-projected mean-field Ansatz for the undoped model is broken upon doping. These variational doped states smoothly connect to the previously studied U(1) π-flux or 0-flux states, and energy minimization among them yields a chiral noncentrosymmetric nematic superconducting state with 2×2-enlarged unit cell. Moreover, this pair density wave state possesses a finite Fermi surface for the Bogoliubov quasiparticles. We further study experimentally relevant properties of this intriguing pairing state.
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Affiliation(s)
- Yi-Fan Jiang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
| | - Hong Yao
- Institute of Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Fan Yang
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
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Pace SD, Morampudi SC, Moessner R, Laumann CR. Emergent Fine Structure Constant of Quantum Spin Ice Is Large. PHYSICAL REVIEW LETTERS 2021; 127:117205. [PMID: 34558951 DOI: 10.1103/physrevlett.127.117205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2021] [Accepted: 07/30/2021] [Indexed: 06/13/2023]
Abstract
Condensed-matter systems provide alternative "vacua" exhibiting emergent low-energy properties drastically different from those of the standard model. A case in point is the emergent quantum electrodynamics (QED) in the fractionalized topological magnet known as quantum spin ice, whose magnetic monopoles set it apart from the familiar QED of the world we live in. Here, we show that the two greatly differ in their fine structure constant α, which parametrizes how strongly matter couples to light: α_{QSI} is more than an order of magnitude greater than α_{QED}≈1/137. Furthermore, α_{QSI}, the emergent speed of light, and all other parameters of the emergent QED, are tunable by engineering the microscopic Hamiltonian. We find that α_{QSI} can be tuned all the way from zero up to what is believed to be the strongest possible coupling beyond which QED confines. In view of the small size of its constrained Hilbert space, this marks out quantum spin ice as an ideal platform for studying exotic quantum field theories and a target for quantum simulation. The large α_{QSI} implies that experiments probing candidate condensed-matter realizations of quantum spin ice should expect to observe phenomena arising due to strong interactions.
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Affiliation(s)
- Salvatore D Pace
- TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - Siddhardh C Morampudi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Roderich Moessner
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - Chris R Laumann
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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18
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Sun K, Mao X. Fractional Excitations in Non-Euclidean Elastic Plates. PHYSICAL REVIEW LETTERS 2021; 127:098001. [PMID: 34506176 DOI: 10.1103/physrevlett.127.098001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 08/03/2021] [Indexed: 06/13/2023]
Abstract
We show that minimal-surface non-Euclidean elastic plates share the same low-energy effective theory as Haldane's dimerized quantum spin chain. As a result, such elastic plates support fractional excitations, which take the form of charge-1/2 solitons between degenerate states of the plate, in strong analogy to their quantum counterpart. These fractional excitations exhibit properties similar to fractional excitations in quantum fractional topological states and in Haldane's dimerized quantum spin chain, including deconfinement and braiding, as well as unique new features such as holographic properties and diodelike nonlinear response, demonstrating great potentials for applications as mechanical metamaterials.
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Affiliation(s)
- Kai Sun
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Xiaoming Mao
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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19
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Jiang HC, Kivelson SA. High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid. PHYSICAL REVIEW LETTERS 2021; 127:097002. [PMID: 34506188 DOI: 10.1103/physrevlett.127.097002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
We have performed density-matrix renormalization group studies of a square lattice t-J model with small hole doping, δ≪1, on long four and six-leg cylinders. We include frustration in the form of a second-neighbor exchange coupling, J_{2}=J_{1}/2, such that the undoped (δ=0) "parent" state is a quantum spin liquid. In contrast to the relatively short range superconducting (SC) correlations that have been observed in recent studies of the six-leg cylinder in the absence of frustration, we find power-law SC correlations with a Luttinger exponent, K_{SC}≈1, consistent with a strongly diverging SC susceptibility, χ∼T^{-(2-K_{SC})} as the temperature T→0. The spin-spin correlations-as in the undoped state-fall exponentially suggesting that the SC "pairing" correlations evolve smoothly from the insulating parent state.
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Affiliation(s)
- Hong-Chen Jiang
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
| | - Steven A Kivelson
- Department of Physics, Stanford University, Stanford, California 94305, USA
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20
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Wilkins N, Powell S. Topological sectors, dimer correlations, and monomers from the transfer-matrix solution of the dimer model. Phys Rev E 2021; 104:014145. [PMID: 34412271 DOI: 10.1103/physreve.104.014145] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Accepted: 06/29/2021] [Indexed: 11/07/2022]
Abstract
We solve the classical square-lattice dimer model with periodic boundaries and in the presence of a field t that couples to the (vector) flux, by diagonalizing a modified version of Lieb's transfer matrix. After deriving the torus partition function in the thermodynamic limit, we show how the configuration space divides into topological sectors corresponding to distinct values of the flux. Additionally, we demonstrate in general that expectation values are t independent at leading order, and obtain explicit expressions for dimer occupation numbers, dimer-dimer correlation functions, and the monomer distribution function. The last of these is expressed as a Toeplitz determinant, whose asymptotic behavior for large monomer separation is tractable using the Fisher-Hartwig conjecture. Our results reproduce those previously obtained using Pfaffian techniques.
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Affiliation(s)
- Neil Wilkins
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Stephen Powell
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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21
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Savary L. Quantum loop states in spin-orbital models on the honeycomb lattice. Nat Commun 2021; 12:3004. [PMID: 34021135 PMCID: PMC8139991 DOI: 10.1038/s41467-021-23033-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 04/05/2021] [Indexed: 11/09/2022] Open
Abstract
The search for truly quantum phases of matter is a center piece of modern research in condensed matter physics. Quantum spin liquids, which host large amounts of entanglement-an entirely quantum feature where one part of a system cannot be measured without modifying the rest-are exemplars of such phases. Here, we devise a realistic model which relies upon the well-known Haldane chain phase, i.e. the phase of spin-1 chains which host fractional excitations at their ends, akin to the hallmark excitations of quantum spin liquids. We tune our model to exactly soluble points, and find that the ground state realizes Haldane chains whose physical supports fluctuate, realizing both quantum spin liquid like and symmetry-protected topological phases. Crucially, this model is expected to describe actual materials, and we provide a detailed set of material-specific constraints which may be readily used for an experimental realization.
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Affiliation(s)
- Lucile Savary
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Université de Lyon, École Normale Supérieure de Lyon, Université Claude Bernard Lyon I, CNRS, Laboratoire de physique, Lyon, France.
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22
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Karpov P, Verdel R, Huang YP, Schmitt M, Heyl M. Disorder-Free Localization in an Interacting 2D Lattice Gauge Theory. PHYSICAL REVIEW LETTERS 2021; 126:130401. [PMID: 33861103 DOI: 10.1103/physrevlett.126.130401] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Revised: 12/24/2020] [Accepted: 02/04/2021] [Indexed: 06/12/2023]
Abstract
Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. This result is all the more surprising since the conventional many-body localization is conjectured to be unstable in two dimensions; hence the gauge invariance represents an alternative robust localization mechanism surviving in higher dimensions in the presence of interactions. Specifically, we demonstrate nonergodic behavior in the quantum link model by obtaining a bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side of the transition. We study the quantum dynamics in this system by introducing the method of "variational classical networks," an efficient and perturbatively controlled representation of the wave function in terms of a network of classical spins akin to artificial neural networks. We identify a distinguishing dynamical signature by studying the propagation of line defects, yielding different light cone structures in the localized and ergodic phases, respectively. The methods we introduce in this work can be applied to any lattice gauge theory with finite-dimensional local Hilbert spaces irrespective of spatial dimensionality.
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Affiliation(s)
- P Karpov
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
- National University of Science and Technology "MISiS," Moscow 119991, Russia
| | - R Verdel
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
| | - Y-P Huang
- The Paul Scherrer Institute, Forschungsstrasse 111, 5232 Villigen, Switzerland
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - M Schmitt
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| | - M Heyl
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
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23
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Causer L, Lesanovsky I, Bañuls MC, Garrahan JP. Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model. Phys Rev E 2020; 102:052132. [PMID: 33327088 DOI: 10.1103/physreve.102.052132] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 11/09/2020] [Indexed: 11/07/2022]
Abstract
We study a one-dimensional classical stochastic kinetically constrained model (KCM) inspired by Rydberg atoms in their "facilitated" regime, where sites can flip only if a single of their nearest neighbors is excited. We call this model "XOR-FA" to distinguish it from the standard Fredrickson-Andersen (FA) model. We describe the dynamics of the XOR-FA model, including its relation to simple exclusion processes in its domain wall representation. The interesting relaxation dynamics of the XOR-FA is related to the prominence of large dynamical fluctuations that lead to phase transitions between active and inactive dynamical phases as in other KCMs. By means of numerical tensor network methods we study in detail such transitions in the dynamical large deviation regime.
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Affiliation(s)
- Luke Causer
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Mari Carmen Bañuls
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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24
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Jiang YF, Jiang HC. Topological Superconductivity in the Doped Chiral Spin Liquid on the Triangular Lattice. PHYSICAL REVIEW LETTERS 2020; 125:157002. [PMID: 33095631 DOI: 10.1103/physrevlett.125.157002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 08/04/2020] [Accepted: 09/15/2020] [Indexed: 06/11/2023]
Abstract
It has long been proposed that doping a chiral spin liquid (CSL) or fractional quantum Hall state can give rise to topological superconductivity. Despite intensive effort, definitive evidences still remain lacking. We address this problem by studying the t-J model supplemented by time-reversal symmetry breaking chiral interaction J_{χ} on the triangular lattice using density-matrix renormalization group with a finite concentration δ of doped holes. It has been established that the undoped, i.e., δ=0, system has a CSL ground state in the parameter region 0.32≤J_{χ}/J≤0.56. Upon light doping, we find that the ground state of the system is consistent with a Luther-Emery liquid with power-law superconducting and charge-density-wave correlations but short-range spin-spin correlations. In particular, the superconducting correlations, whose pairing symmetry is consistent with d±id wave, are dominant at all hole doping concentrations. Our results provide direct evidences that doping the CSL on the triangular lattice can naturally give rise to topological superconductivity.
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Affiliation(s)
- Yi-Fan Jiang
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
| | - Hong-Chen Jiang
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
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25
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Klishin AA, van Anders G. When does entropy promote local organization? SOFT MATTER 2020; 16:6523-6531. [PMID: 32597444 DOI: 10.1039/c9sm02540e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Crowded soft-matter and biological systems organize locally into preferred motifs. Locally-organized motifs in soft systems can, paradoxically, arise from a drive to maximize overall system entropy. Entropy-driven local order has been directly confirmed in model, synthetic colloidal systems, however similar patterns of organization occur in crowded biological systems ranging from the contents of a cell to collections of cells. In biological settings, and in soft matter more broadly, it is unclear whether entropy generically promotes or inhibits local organization. Resolving this is difficult because entropic effects are intrinsically collective, complicating efforts to isolate them. Here, we employ minimal models that artificially restrict system entropy to show that entropy drives systems toward local organization, even when the model system entropy is below reasonable physical bounds. By establishing this bound, our results suggest that entropy generically promotes local organization in crowded soft and biological systems of rigid objects.
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Affiliation(s)
- Andrei A Klishin
- Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
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26
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Cardarelli L, Greschner S, Santos L. Deconfining Disordered Phase in Two-Dimensional Quantum Link Models. PHYSICAL REVIEW LETTERS 2020; 124:123601. [PMID: 32281853 DOI: 10.1103/physrevlett.124.123601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
We explore the ground-state physics of two-dimensional spin-1/2 U(1) quantum link models, one of the simplest nontrivial lattice gauge theories with fermionic matter within experimental reach for quantum simulations. Whereas in the large mass limit we observe Neél-like vortex-antivortex and striped crystalline phases, for small masses there is a transition from the striped phases into a disordered phase whose properties resemble those at the Rokhsar-Kivelson point of the quantum dimer model. This phase is characterized on ladders by boundary Haldane-like properties, such as vanishing parity and finite string ordering. Moreover, from studies of the string tension between gauge charges, we find that, whereas the striped phases are confined, the novel disordered phase present clear indications of being deconfined. Our results open exciting perspectives of studying highly nontrivial physics in quantum simulators, such as spin-liquid behavior and confinement-deconfinement transitions, without the need of explicitly engineering plaquette terms.
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Affiliation(s)
- Lorenzo Cardarelli
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, DE-30167 Hannover, Germany
| | - Sebastian Greschner
- Department of Quantum Matter Physics, University of Geneva, CH-1211 Geneva, Switzerland
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, DE-30167 Hannover, Germany
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27
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Broholm C, Cava RJ, Kivelson SA, Nocera DG, Norman MR, Senthil T. Quantum spin liquids. Science 2020; 367:367/6475/eaay0668. [DOI: 10.1126/science.aay0668] [Citation(s) in RCA: 271] [Impact Index Per Article: 67.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- C. Broholm
- Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA
| | - R. J. Cava
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
| | - S. A. Kivelson
- Department of Physics, Stanford University, Stanford, CA 94305, USA
| | - D. G. Nocera
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
| | - M. R. Norman
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA
| | - T. Senthil
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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28
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Feldmeier J, Pollmann F, Knap M. Emergent Glassy Dynamics in a Quantum Dimer Model. PHYSICAL REVIEW LETTERS 2019; 123:040601. [PMID: 31491242 DOI: 10.1103/physrevlett.123.040601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Revised: 05/27/2019] [Indexed: 06/10/2023]
Abstract
We consider the quench dynamics of a two-dimensional quantum dimer model and determine the role of its kinematic constraints. We interpret the nonequilibrium dynamics in terms of the underlying equilibrium phase transitions consisting of a Berezinskii-Kosterlitz-Thouless (BKT) transition between a columnar ordered valence bond solid (VBS) and a valence bond liquid (VBL), as well as a first-order transition between a staggered VBS and the VBL. We find that quenches from a columnar VBS are ergodic and both order parameters and spatial correlations quickly relax to their thermal equilibrium. By contrast, the staggered side of the first-order transition does not display thermalization on numerically accessible timescales. Based on the model's kinematic constraints, we uncover a mechanism of relaxation that rests on emergent, highly detuned multidefect processes in a staggered background, which gives rise to slow, glassy dynamics at low temperatures even in the thermodynamic limit.
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Affiliation(s)
- Johannes Feldmeier
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Frank Pollmann
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Michael Knap
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
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29
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Huang YP, Banerjee D, Heyl M. Dynamical Quantum Phase Transitions in U(1) Quantum Link Models. PHYSICAL REVIEW LETTERS 2019; 122:250401. [PMID: 31347880 DOI: 10.1103/physrevlett.122.250401] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Revised: 03/15/2019] [Indexed: 06/10/2023]
Abstract
Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. QLMs not only reproduce standard features of Wilson lattice gauge theories in equilibrium, but can also host new phenomena such as crystalline confined phases. The local constraints due to gauge invariance also provide kinetic restrictions that can influence substantially the real-time dynamics in these systems. We aim to characterize the nonequilibrium evolution in lattice gauge theories through the lens of dynamical quantum phase transitions, which provide general principles for real-time dynamics in quantum many-body systems. Specifically, we study quantum quenches for two representative cases, U(1) QLMs in (1+1)D and (2+1)D, for initial conditions exhibiting long-range order. Finally, we discuss the connection to the high-energy perspective and the experimental feasibility to observe the discussed phenomena in recent quantum simulator settings such as trapped ions, ultracold atoms, and Rydberg atoms.
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Affiliation(s)
- Yi-Ping Huang
- Max-Planck-Institut fur Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Debasish Banerjee
- Max-Planck-Institut fur Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Markus Heyl
- Max-Planck-Institut fur Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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30
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Zhu GY, Zhang GM. Gapless Coulomb State Emerging from a Self-Dual Topological Tensor-Network State. PHYSICAL REVIEW LETTERS 2019; 122:176401. [PMID: 31107080 DOI: 10.1103/physrevlett.122.176401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2019] [Indexed: 06/09/2023]
Abstract
In the tensor network representation, a deformed Z_{2} topological ground state wave function is proposed and its norm can be exactly mapped to the two-dimensional solvable Ashkin-Teller model. Then the topological (toric code) phase with anyonic excitations corresponds to the partial order phase of the Ashkin-Teller model, and possible topological phase transitions are precisely determined. With the electric-magnetic self-duality, a novel gapless Coulomb state with quasi-long-range order is obtained via a quantum Kosterlitz-Thouless phase transition. The corresponding ground state is a condensate of pairs of logarithmically confined electric charges and magnetic fluxes, and the scaling behavior of various anyon correlations can be exactly derived, revealing the effective interaction between anyons and their condensation. Deformations away from the self-duality drive the Coulomb state into either the gapped Higgs phase or the confining phase.
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Affiliation(s)
- Guo-Yi Zhu
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Guang-Ming Zhang
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
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31
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Chen CN, Hu CK, Izmailian NS, Wu MC. Specific heat and partition function zeros for the dimer model on the checkerboard B lattice: Finite-size effects. Phys Rev E 2019; 99:012102. [PMID: 30780272 DOI: 10.1103/physreve.99.012102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Indexed: 06/09/2023]
Abstract
There are three possible classifications of the dimer weights on the bonds of the checkerboard lattice and they are denoted as checkerboard A, B, and C lattices [Phys. Rev. E 91, 062139 (2015)PLEEE81539-375510.1103/PhysRevE.91.062139]. The dimer model on the checkerboard B and C lattices has much richer critical behavior compared to the dimer model on the checkerboard A lattice. In this paper we study in full detail the dimer model on the checkerboard B lattice. The dimer model on the checkerboard B lattice has two types of critical behavior. In one limit this model is the anisotropic dimer model on rectangular lattice with algebraic decay of correlators and in another limit it is the anisotropic generalized Kasteleyn model with radically different critical behavior. We analyze the partition function of the dimer model on a 2M×2N checkerboard B lattice wrapped on a torus. We find very unusual behavior of the partition function zeros and the specific heat of the dimer model. Remarkably, the partition function zeros of finite-size systems can have very interesting structures, made of rings, concentric circles, radial line segments, or even arabesque structures. We find out that the number of the specific heat peaks and the number of circles of the partition function zeros increases with the system size. The lattice anisotropy of the model has strong effects on the behavior of the specific heat, dominating the relation between the correlation length exponent ν and the shift exponent λ, and λ is generally unequal to 1/ν (λ≠1/ν).
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Affiliation(s)
- Chi-Ning Chen
- Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan
| | - Chin-Kun Hu
- Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
| | - N Sh Izmailian
- Yerevan Physics Institute, Alikhanian Brothers 2, 375036 Yerevan, Armenia
| | - Ming-Chya Wu
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
- Research Center for Adaptive Data Analysis, National Central University, Zhongli, Taoyuan 32001, Taiwan
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32
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Sachdev S. Topological order, emergent gauge fields, and Fermi surface reconstruction. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:014001. [PMID: 30210062 DOI: 10.1088/1361-6633/aae110] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This review describes how topological order associated with the presence of emergent gauge fields can reconstruct Fermi surfaces of metals, even in the absence of translational symmetry breaking. We begin with an introduction to topological order using Wegner's quantum [Formula: see text] gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying [Formula: see text] magnetic flux. The interplay between topological order and the breaking of global symmetry is described by the non-zero temperature statistical mechanics of classical XY models in dimension D = 3; such models also describe the zero temperature quantum phases of bosons with short-range interactions on the square lattice at integer filling. The topological state is again characterized by the expulsion of certain defects, in a state with fluctuating symmetry-breaking order, along with the presence of emergent gauge fields. The phase diagrams of the [Formula: see text] gauge theory and the XY models are obtained by embedding them in U(1) gauge theories, and by studying their Higgs and confining phases. These ideas are then applied to the single-band Hubbard model on the square lattice. A SU(2) gauge theory describes the fluctuations of spin-density-wave order, and its phase diagram is presented by analogy to the XY models. We obtain a class of zero temperature metallic states with fluctuating spin-density wave order, topological order associated with defect expulsion, deconfined emergent gauge fields, reconstructed Fermi surfaces (with 'chargon' or electron-like quasiparticles), but no broken symmetry. We conclude with the application of such metallic states to the pseudogap phase of the cuprates, and note the recent comparison with numerical studies of the Hubbard model and photoemission observations of the electron-doped cuprates. In a detour, we also discuss the influence of Berry phases, and how they can lead to deconfined quantum critical points: this applies to bosons on the square lattice at half-integer filling, and to quantum dimer models.
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Affiliation(s)
- Subir Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, United States of America. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada. Department of Physics, Stanford University, Stanford, CA 94305, United States of America
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Chen C, Burnell F, Chandran A. How Does a Locally Constrained Quantum System Localize? PHYSICAL REVIEW LETTERS 2018; 121:085701. [PMID: 30192622 DOI: 10.1103/physrevlett.121.085701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2017] [Indexed: 06/08/2023]
Abstract
At low energy, the dynamics of excitations of many physical systems are locally constrained. Examples include frustrated antiferromagnets, fractional quantum Hall fluids, and Rydberg atoms in the blockaded regime. Can such locally constrained systems be fully many-body localized? In this Letter, we answer this question affirmatively and elucidate the structure of the accompanying quasilocal integrals of motion. By studying disordered spin chains subject to a projection constraint in the z direction, we show that full many-body localization (MBL) is stable at strong z-field disorder and identify a new mechanism of localization through resonance at strong transverse disorder. However, MBL is not guaranteed; the constraints can "frustrate" the tendency of the spins to align with the transverse fields and lead to full thermalization or criticality. We further provide evidence that the transition is discontinuous in local observables with large sample-to-sample variations. Our dynamical phase diagram is accessible in current Rydberg atomic experiments which realize programmable constrained Ising Hamiltonians.
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Affiliation(s)
- Chun Chen
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Fiona Burnell
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Anushya Chandran
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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34
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Benton O, Jaubert LDC, Singh RRP, Oitmaa J, Shannon N. Quantum Spin Ice with Frustrated Transverse Exchange: From a π-Flux Phase to a Nematic Quantum Spin Liquid. PHYSICAL REVIEW LETTERS 2018; 121:067201. [PMID: 30141668 DOI: 10.1103/physrevlett.121.067201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2018] [Indexed: 06/08/2023]
Abstract
Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalization, numerical linked-cluster and series expansions, we find that the previously studied U(1) quantum spin liquid, in its π-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.
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Affiliation(s)
- Owen Benton
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - L D C Jaubert
- CNRS, Université de Bordeaux, LOMA, UMR 5798, 33400 Talence, France
| | - Rajiv R P Singh
- Department of Physics, University of California, Davis, California 95616, USA
| | - Jaan Oitmaa
- School of Physics, The University of New South Wales, Sydney 2052, Australia
| | - Nic Shannon
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
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35
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Lan Z, van Horssen M, Powell S, Garrahan JP. Quantum Slow Relaxation and Metastability due to Dynamical Constraints. PHYSICAL REVIEW LETTERS 2018; 121:040603. [PMID: 30095948 DOI: 10.1103/physrevlett.121.040603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Revised: 05/24/2018] [Indexed: 06/08/2023]
Abstract
One of the general mechanisms that give rise to the slow cooperative relaxation characteristic of classical glasses is the presence of kinetic constraints in the dynamics. Here we show that dynamical constraints can similarly lead to slow thermalization and metastability in translationally invariant quantum many-body systems. We illustrate this general idea by considering two simple models: (i) a one-dimensional quantum analogue to classical constrained lattice gases where excitation hopping is constrained by the state of neighboring sites, mimicking excluded-volume interactions of dense fluids; and (ii) fully packed quantum dimers on the square lattice. Both models have a Rokhsar-Kivelson (RK) point at which kinetic and potential energy constants are equal. To one side of the RK point, where kinetic energy dominates, thermalization is fast. To the other, where potential energy dominates, thermalization is slow, memory of initial conditions persists for long times, and separation of timescales leads to pronounced metastability before eventual thermalization. Furthermore, in analogy with what occurs in the relaxation of classical glasses, the slow-thermalization regime displays dynamical heterogeneity as manifested by spatially segregated growth of entanglement.
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Affiliation(s)
- Zhihao Lan
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems and School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Merlijn van Horssen
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems and School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Stephen Powell
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems and School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems and School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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36
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Benton O. Instabilities of a U(1) Quantum Spin Liquid in Disordered Non-Kramers Pyrochlores. PHYSICAL REVIEW LETTERS 2018; 121:037203. [PMID: 30085790 DOI: 10.1103/physrevlett.121.037203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Revised: 04/06/2018] [Indexed: 06/08/2023]
Abstract
Quantum spin liquids (QSLs) are exotic phases of matter exhibiting long-range entanglement and supporting emergent gauge fields. A vigorous search for experimental realizations of these states has identified several materials with properties hinting at QSL physics. A key issue in understanding these QSL candidates is often the interplay of weak disorder of the crystal structure with the spin liquid state. It has recently been pointed out that in at least one important class of candidate QSLs-pyrochlore magnets based on non-Kramers ions such as Pr^{3+} or Tb^{3+}-structural disorder can actually promote a U(1) QSL ground state. Here we set this proposal on a quantitative footing by analyzing the stability of the QSL state in the minimal model for these systems: a random transverse field Ising model. We consider two kinds of instability, which are relevant in different limits of the phase diagram: condensation of spinons and confinement of the U(1) gauge fields. Having obtained stability bounds on the QSL state, we apply our results directly to the disordered candidate QSL Pr_{2}Zr_{2}O_{7}. We find that the available data for currently studied samples of Pr_{2}Zr_{2}O_{7} are most consistent with it a ground state outside the spin liquid regime, in a paramagnetic phase with quadrupole moments near saturation due to the influence of structural disorder.
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Affiliation(s)
- Owen Benton
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama, 351-0198, Japan
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Feldmeier J, Huber S, Punk M. Exact Solution of a Two-Species Quantum Dimer Model for Pseudogap Metals. PHYSICAL REVIEW LETTERS 2018; 120:187001. [PMID: 29775366 DOI: 10.1103/physrevlett.120.187001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Indexed: 06/08/2023]
Abstract
We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015).PNASA60027-842410.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-T_{c} cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.
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Affiliation(s)
- Johannes Feldmeier
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-University Munich, 80333 Munich, Germany
| | - Sebastian Huber
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-University Munich, 80333 Munich, Germany
| | - Matthias Punk
- Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-University Munich, 80333 Munich, Germany
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38
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Abstract
Quantum spin liquids (QSLs) have been at the forefront of correlated electron research ever since their proposal in 1973, and the realization that they belong to the broader class of intrinsic topological orders. According to received wisdom, QSLs can arise in frustrated magnets with low spin S, where strong quantum fluctuations act to destabilize conventional, magnetically ordered states. Here, we present a Z2 QSL ground state that appears already in the semiclassical, large-S limit. This state has both topological and symmetry-related ground-state degeneracy, and two types of gaps, a “magnetic flux” gap that scales linearly with S and an “electric charge” gap that drops exponentially in S. The magnet is the spin-S version of the spin-1/2 Kitaev honeycomb model, which has been the subject of intense studies in correlated electron systems with strong spin–orbit coupling, and in optical lattice realizations with ultracold atoms. Strongly correlated quantum spin liquid phases form when quantum fluctuations prevent magnetic ordering, which normally requires low spin systems that cannot be analyzed semiclassically. Here, the authors show that a large-spin Kitaev model supports a spin liquid phase in the semiclassical limit.
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39
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Jiang HC, Devereaux T, Kivelson SA. Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid. PHYSICAL REVIEW LETTERS 2017; 119:067002. [PMID: 28949592 DOI: 10.1103/physrevlett.119.067002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2017] [Indexed: 06/07/2023]
Abstract
We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t-J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ=0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole per unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. Our results may be relevant to kagome lattice herbertsmithite upon doping.
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Affiliation(s)
- Hong-Chen Jiang
- Stanford Institute for Materials and Energy Sciences, SLAC and Stanford University, Menlo Park, California 94025, USA
| | - T Devereaux
- Stanford Institute for Materials and Energy Sciences, SLAC and Stanford University, Menlo Park, California 94025, USA
| | - S A Kivelson
- Department of Physics, Stanford University, Stanford, California 94305, USA
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40
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Iemini F, Mora C, Mazza L. Topological Phases of Parafermions: A Model with Exactly Solvable Ground States. PHYSICAL REVIEW LETTERS 2017; 118:170402. [PMID: 28498698 DOI: 10.1103/physrevlett.118.170402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2016] [Indexed: 06/07/2023]
Abstract
Parafermions are emergent excitations that generalize Majorana fermions and can also realize topological order. In this Letter, we present a nontrivial and quasi-exactly-solvable model for a chain of parafermions in a topological phase. We compute and characterize the ground-state wave functions, which are matrix-product states and have a particularly elegant interpretation in terms of Fock parafermions, reflecting the factorized nature of the ground states. Using these wave functions, we demonstrate analytically several signatures of topological order. Our study provides a starting point for the nonapproximate study of topological one-dimensional parafermionic chains with spatial inversion and time-reversal symmetry in the absence of strong edge modes.
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Affiliation(s)
- Fernando Iemini
- ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Christophe Mora
- Laboratoire Pierre Aigrain, École Normale Supérieure/PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
| | - Leonardo Mazza
- Département de Physique, École Normale Supérieure/PSL Research University, CNRS, 24 rue Lhomond, F-75005 Paris, France
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41
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Savary L, Balents L. Quantum spin liquids: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:016502. [PMID: 27823986 DOI: 10.1088/0034-4885/80/1/016502] [Citation(s) in RCA: 283] [Impact Index Per Article: 40.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.
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Affiliation(s)
- Lucile Savary
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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42
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Izmailian NS, Wu MC, Hu CK. Finite-size corrections and scaling for the dimer model on the checkerboard lattice. Phys Rev E 2016; 94:052141. [PMID: 27967158 DOI: 10.1103/physreve.94.052141] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2016] [Indexed: 12/30/2022]
Abstract
Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function of the dimer model on a 2M×2N checkerboard lattice wrapped on a torus and derive the exact asymptotic expansion of the logarithm of the partition function. We find that the internal energy at the critical point is equal to zero. We also derive the exact finite-size corrections for the free energy, the internal energy, and the specific heat. Using the exact partition function and finite-size corrections for the dimer model on a finite checkerboard lattice, we obtain finite-size scaling functions for the free energy, the internal energy, and the specific heat of the dimer model. We investigate the properties of the specific heat near the critical point and find that the specific-heat pseudocritical point coincides with the critical point of the thermodynamic limit, which means that the specific-heat shift exponent λ is equal to ∞. We have also considered the limit N→∞ for which we obtain the expansion of the free energy for the dimer model on the infinitely long cylinder. From a finite-size analysis we have found that two conformal field theories with the central charges c=1 for the height function description and c=-2 for the construction using a mapping of spanning trees can be used to describe the dimer model on the checkerboard lattice.
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Affiliation(s)
| | - Ming-Chya Wu
- Research Center for Adaptive Data Analysis, National Central University, Zhongli, Taoyuan 32001, Taiwan.,Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
| | - Chin-Kun Hu
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.,National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu 30013, Taiwan.,Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
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43
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Brennen GK, Pupillo G, Rico E, Stace TM, Vodola D. Loops and Strings in a Superconducting Lattice Gauge Simulator. PHYSICAL REVIEW LETTERS 2016; 117:240504. [PMID: 28009201 DOI: 10.1103/physrevlett.117.240504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Indexed: 06/06/2023]
Abstract
We propose an architecture for an analog quantum simulator of electromagnetism in 2+1 dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1) representation of the quantum link model formulation of compact U(1) lattice gauge theory. We show how to engineer Gauss' law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from 't Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.
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Affiliation(s)
- G K Brennen
- Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia
| | - G Pupillo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Universite de Strasbourg and CNRS,67000 Strasbourg, France
| | - E Rico
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain
| | - T M Stace
- Center for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland 4072, Australia
| | - D Vodola
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Universite de Strasbourg and CNRS,67000 Strasbourg, France
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44
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Nataf P, Lajkó M, Wietek A, Penc K, Mila F, Läuchli AM. Chiral Spin Liquids in Triangular-Lattice SU(N) Fermionic Mott Insulators with Artificial Gauge Fields. PHYSICAL REVIEW LETTERS 2016; 117:167202. [PMID: 27792381 DOI: 10.1103/physrevlett.117.167202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Indexed: 06/06/2023]
Abstract
We show that, in the presence of a π/2 artificial gauge field per plaquette, Mott insulating phases of ultracold fermions with SU(N) symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by an approximate ground space of N low-lying singlets for periodic boundary conditions, and by chiral edge states described by the SU(N)_{1} Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for N between 3 and 9, and by a parton construction based on a set of N Gutzwiller projected fermionic wave functions with flux π/N per triangular plaquette. Experimental implications are briefly discussed.
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Affiliation(s)
- Pierre Nataf
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Miklós Lajkó
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - Alexander Wietek
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Karlo Penc
- Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, H-1525 Budapest, P.O.B. 49, Hungary
- MTA-BME Lendület Magneto-optical Spectroscopy Research Group, 1111 Budapest, Hungary
| | - Frédéric Mila
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Andreas M Läuchli
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
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45
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Takatsu H, Onoda S, Kittaka S, Kasahara A, Kono Y, Sakakibara T, Kato Y, Fåk B, Ollivier J, Lynn JW, Taniguchi T, Wakita M, Kadowaki H. Quadrupole Order in the Frustrated Pyrochlore Tb_{2+x}Ti_{2-x}O_{7+y}. PHYSICAL REVIEW LETTERS 2016; 116:217201. [PMID: 27284670 DOI: 10.1103/physrevlett.116.217201] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2015] [Indexed: 06/06/2023]
Abstract
A hidden order that emerges in the frustrated pyrochlore Tb_{2+x}Ti_{2-x}O_{7+y} with T_{c}=0.53 K is studied using specific heat, magnetization, and neutron scattering experiments on a high-quality single crystal. Semiquantitative analyses based on a pseudospin-1/2 Hamiltonian for ionic non-Kramers magnetic doublets demonstrate that it is an ordered state of electric quadrupole moments. The elusive spin liquid state of the nominal Tb_{2}Ti_{2}O_{7} is most likely a U(1) quantum spin-liquid state.
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Affiliation(s)
- H Takatsu
- Department of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan
- Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
| | - S Onoda
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan
| | - S Kittaka
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - A Kasahara
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - Y Kono
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - T Sakakibara
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - Y Kato
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Department of Applied Physics, University of Tokyo, Bunkyo, Tokyo 113-8656, Japan
| | - B Fåk
- Institute Laue Langevin, BP 156, F-38042 Grenoble, France
| | - J Ollivier
- Institute Laue Langevin, BP 156, F-38042 Grenoble, France
| | - J W Lynn
- NCNR, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-6102, USA
| | - T Taniguchi
- Department of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan
| | - M Wakita
- Department of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan
| | - H Kadowaki
- Department of Physics, Tokyo Metropolitan University, Hachioji-shi, Tokyo 192-0397, Japan
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46
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Abstract
A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
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47
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Wan Y, Carrasquilla J, Melko RG. Spinon Walk in Quantum Spin Ice. PHYSICAL REVIEW LETTERS 2016; 116:167202. [PMID: 27152822 DOI: 10.1103/physrevlett.116.167202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2015] [Indexed: 06/05/2023]
Abstract
We study a minimal model for the dynamics of spinons in quantum spin ice. The model captures the essential strong coupling between the spinon and the disordered background spins. We demonstrate that the spinon motion can be mapped to a random walk with an entropy-induced memory in imaginary time. Our numerical simulation of the spinon walk indicates that the spinon propagates as a massive quasiparticle at low energy despite its strong coupling to the spin background at the microscopic energy scale. We discuss the experimental implications of our findings.
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Affiliation(s)
- Yuan Wan
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - Juan Carrasquilla
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - Roger G Melko
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
- Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada
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Gosset D, Huang Y. Correlation Length versus Gap in Frustration-Free Systems. PHYSICAL REVIEW LETTERS 2016; 116:097202. [PMID: 26991196 DOI: 10.1103/physrevlett.116.097202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2015] [Indexed: 06/05/2023]
Abstract
Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap ε has correlation length ξ upper bounded as ξ=O(1/ε). In general this bound cannot be improved. Here we study the scaling of the correlation length as a function of the spectral gap in frustration-free local Hamiltonians, and we prove a tight bound ξ=O(1/sqrt[ε]) in this setting. This highlights a fundamental difference between frustration-free and frustrated systems near criticality. The result is obtained using an improved version of the combinatorial proof of correlation decay due to Aharonov, Arad, Vazirani, and Landau.
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Affiliation(s)
- David Gosset
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Yichen Huang
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
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Yang ZC, Chamon C, Hamma A, Mucciolo ER. Two-Component Structure in the Entanglement Spectrum of Highly Excited States. PHYSICAL REVIEW LETTERS 2015; 115:267206. [PMID: 26765022 DOI: 10.1103/physrevlett.115.267206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Indexed: 06/05/2023]
Abstract
We study the entanglement spectrum of highly excited eigenstates of two known models that exhibit a many-body localization transition, namely the one-dimensional random-field Heisenberg model and the quantum random energy model. Our results indicate that the entanglement spectrum shows a "two-component" structure: a universal part that is associated with random matrix theory, and a nonuniversal part that is model dependent. The nonuniversal part manifests the deviation of the highly excited eigenstate from a true random state even in the thermalized phase where the eigenstate thermalization hypothesis holds. The fraction of the spectrum containing the universal part decreases as one approaches the critical point and vanishes in the localized phase in the thermodynamic limit. We use the universal part fraction to construct an order parameter for measuring the degree of randomness of a generic highly excited state, which is also a promising candidate for studying the many-body localization transition. Two toy models based on Rokhsar-Kivelson type wave functions are constructed and their entanglement spectra are shown to exhibit the same structure.
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Affiliation(s)
- Zhi-Cheng Yang
- Physics Department, Boston University, Boston, Massachusetts 02215, USA
| | - Claudio Chamon
- Physics Department, Boston University, Boston, Massachusetts 02215, USA
| | - Alioscia Hamma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Eduardo R Mucciolo
- Department of Physics, University of Central Florida, Orlando, Florida 32816, USA
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He YC, Bhattacharjee S, Pollmann F, Moessner R. Kagome Chiral Spin Liquid as a Gauged U(1) Symmetry Protected Topological Phase. PHYSICAL REVIEW LETTERS 2015; 115:267209. [PMID: 26765025 DOI: 10.1103/physrevlett.115.267209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2015] [Indexed: 06/05/2023]
Abstract
While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.
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Affiliation(s)
- Yin-Chen He
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Subhro Bhattacharjee
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012, India
| | - Frank Pollmann
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - R Moessner
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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