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Song H, Tantivasadakarn N, Shirley W, Hermele M. Fracton Self-Statistics. Phys Rev Lett 2024; 132:016604. [PMID: 38242667 DOI: 10.1103/physrevlett.132.016604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 12/14/2023] [Indexed: 01/21/2024]
Abstract
Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility and, thus, lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating multiple excitations are called fractons. Here, we address a fundamental open question-can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged and show that their self-statistics is a key part of the characterization of fracton orders. We derive general constraints satisfied by the fracton self-statistics in a large class of Abelian fracton orders. Finally, we show the existence of nontrivial fracton self-statistics in some twisted variants of the checkerboard model and Haah's code, establishing that these models are in distinct quantum phases as compared to their untwisted cousins.
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Affiliation(s)
- Hao Song
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Nathanan Tantivasadakarn
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Wilbur Shirley
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
- School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Michael Hermele
- Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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Abstract
Motivated by the prediction of fractonic topological defects in a quantum crystal, we utilize a reformulated elasticity duality to derive a description of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton order and restricted mobility emerge as a result of an unusual Gauss law where electric field lines of one gauge field act as sources of charge for others. At low energies this vector gauge theory reduces to the previously studied fractonic symmetric tensor gauge theory. We construct the corresponding lattice model and a number of generalizations, which realize fracton phases via a condensation of stringlike excitations built out of charged particles, analogous to the p-string condensation mechanism of the gapped X-cube fracton phase.
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Affiliation(s)
- Leo Radzihovsky
- Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Michael Hermele
- Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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Abstract
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups. This enumeration gives topological crystalline insulators a full classification.
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Affiliation(s)
- Zhida Song
- Beijing National Research Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Sheng-Jie Huang
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
| | - Yang Qi
- Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China
- State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - Chen Fang
- Beijing National Research Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, Beijing, China
| | - Michael Hermele
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
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Huang YP, Chen G, Hermele M. Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice. Phys Rev Lett 2014; 112:167203. [PMID: 24815666 DOI: 10.1103/physrevlett.112.167203] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2013] [Indexed: 06/03/2023]
Abstract
We consider a class of d- and f-electron systems in which dipolar-octupolar Kramers doublets arise on the sites of the pyrochlore lattice. For such doublets, two components of the pseudospin transform like a magnetic dipole, while the other transforms like a component of the magnetic octupole tensor. Based on a symmetry analysis, we construct and study models of dipolar-octupolar doublets in itinerant and localized limits. In both limits, the resulting models are of surprisingly simple form. In the itinerant limit, we find topological insulating behavior. In the localized limit, the most general nearest-neighbor spin model is the XYZ model. We show that this XYZ model exhibits two distinct quantum spin ice (QSI) phases, that we dub dipolar QSI, and octupolar QSI. We conclude with a discussion of potential relevance to real material systems.
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Affiliation(s)
- Yi-Ping Huang
- Department of Physics, 390 UCB, University of Colorado, Boulder, Colorado 80309, USA
| | - Gang Chen
- Department of Physics, 390 UCB, University of Colorado, Boulder, Colorado 80309, USA
| | - Michael Hermele
- Department of Physics, 390 UCB, University of Colorado, Boulder, Colorado 80309, USA
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Chen G, Hermele M, Radzihovsky L. Frustrated quantum critical theory of putative spin-liquid phenomenology in 6H-B-Ba(3)NiSb(2)O(9). Phys Rev Lett 2012; 109:016402. [PMID: 23031118 DOI: 10.1103/physrevlett.109.016402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2012] [Revised: 04/01/2012] [Indexed: 06/01/2023]
Abstract
A recently discovered material, 6H-B-Ba(3)NiSb(2)O(9) was found to display unusual low-temperature phenomenology, interpreted as a quantum spin liquid with spin S=1 on a triangular lattice. We study a spin S=1 exchange model on an AB stacked triangular lattice near its quantum paramagnet-to-spiral transition, driven by easy-plane single-ion anisotropy. We demonstrate that the frustrated inter- and intralayer exchanges induce contour lines of low-energy excitations that lead to a broad crossover regime of linear-temperature dependence of the specific heat. Based on this and various other predictions, we argue that the observed phenomenology can be understood in terms of a conventional picture of a proximity to this frustrated critical point.
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Affiliation(s)
- G Chen
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
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Hermele M, Gurarie V, Rey AM. Mott insulators of ultracold fermionic alkaline Earth atoms: underconstrained magnetism and chiral spin liquid. Phys Rev Lett 2009; 103:135301. [PMID: 19905520 DOI: 10.1103/physrevlett.103.135301] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2009] [Revised: 08/13/2009] [Indexed: 05/28/2023]
Abstract
We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.
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Affiliation(s)
- Michael Hermele
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
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Ran Y, Hermele M, Lee PA, Wen XG. Projected-wave-function study of the spin-1/2 Heisenberg model on the Kagomé lattice. Phys Rev Lett 2007; 98:117205. [PMID: 17501088 DOI: 10.1103/physrevlett.98.117205] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2006] [Indexed: 05/15/2023]
Abstract
We perform a Gutzwiller projected-wave-function study for the spin-1/2 Heisenberg model on the Kagomé lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization. We show that such a U(1)-Dirac state represents a quantum phase whose low-energy physics is governed by four flavors of two-component Dirac fermions coupled to a U(1) gauge field. These results are discussed in the context of recent experiments on ZnCu(3)(OH)(6)Cl(2).
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Affiliation(s)
- Ying Ran
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Büchler HP, Hermele M, Huber SD, Fisher MPA, Zoller P. Atomic quantum simulator for lattice gauge theories and ring exchange models. Phys Rev Lett 2005; 95:040402. [PMID: 16090783 DOI: 10.1103/physrevlett.95.040402] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2005] [Indexed: 05/03/2023]
Abstract
We present the design of a ring exchange interaction in cold atomic gases subjected to an optical lattice using well-understood tools for manipulating and controlling such gases. The strength of this interaction can be tuned independently and describes the correlated hopping of two bosons. We discuss a setup where this coupling term may allow for the realization and observation of exotic quantum phases, including a deconfined insulator described by the Coulomb phase of a three-dimensional U(1) lattice gauge theory.
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Affiliation(s)
- H P Büchler
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Science, Innsbruck
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