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Papastathopoulos-Katsaros A, Henderson TM, Scuseria GE. Linear Combinations of Cluster Mean-Field States Applied to Spin Systems. J Chem Theory Comput 2024; 20:3697-3705. [PMID: 38695526 DOI: 10.1021/acs.jctc.4c00171] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2024]
Abstract
We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field states and apply it to describe the ground state of strongly correlated spin systems. In cluster mean-field theory, the ground state wave function is expressed as a factorized tensor product of optimized cluster states. While our prior work concentrated on a single cMF tiling, this study removes that constraint by combining different tilings of cMF states. Selection criteria, including translational symmetry and spatial proximity, guide this process. We present benchmark calculations for the one- and two-dimensional J1 - J2 and XXZ Heisenberg models. Our findings highlight two key aspects. First, the method offers a semiquantitative description of the 0.4 ≲ J2/J1 ≲ 0.6 regime of the J1 - J2 model─a particularly challenging regime for existing methods. Second, our results demonstrate the capability of our method to provide qualitative descriptions for all the models and regimes considered, establishing it as a valuable reference. However, the inclusion of additional (weak) correlations is necessary for quantitative agreement, and we explore methods to incorporate these extra correlations.
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Affiliation(s)
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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2
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Papastathopoulos-Katsaros A, Henderson TM, Scuseria GE. Symmetry-projected cluster mean-field theory applied to spin systems. J Chem Phys 2023; 159:084107. [PMID: 37610020 DOI: 10.1063/5.0155765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2023] [Accepted: 07/11/2023] [Indexed: 08/24/2023] Open
Abstract
We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 - J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.
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Affiliation(s)
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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3
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Papastathopoulos-Katsaros A, Jiménez-Hoyos CA, Henderson TM, Scuseria GE. Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems. J Chem Theory Comput 2022; 18:4293-4303. [PMID: 35729717 DOI: 10.1021/acs.jctc.2c00338] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J1-J2 Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.
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Affiliation(s)
| | - Carlos A Jiménez-Hoyos
- Department of Chemistry, Wesleyan University, Middletown, Connecticut 06459, United States
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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4
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Nomura Y. Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:174003. [PMID: 33530063 DOI: 10.1088/1361-648x/abe268] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 02/02/2021] [Indexed: 06/12/2023]
Abstract
The variational wave functions based on neural networks have recently started to be recognized as a powerful ansatz to represent quantum many-body states accurately. In order to show the usefulness of the method among all available numerical methods, it is imperative to investigate the performance in challenging many-body problems for which the exact solutions are not available. Here, we construct a variational wave function with one of the simplest neural networks, the restricted Boltzmann machine (RBM), and apply it to a fundamental but unsolved quantum spin Hamiltonian, the two-dimensionalJ1-J2Heisenberg model on the square lattice. We supplement the RBM wave function with quantum-number projections, which restores the symmetry of the wave function and makes it possible to calculate excited states. Then, we perform a systematic investigation of the performance of the RBM. We show that, with the help of the symmetry, the RBM wave function achieves state-of-the-art accuracy both in ground-state and excited-state calculations. The study shows a practical guideline on how we achieve accuracy in a controlled manner.
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Affiliation(s)
- Yusuke Nomura
- RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
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5
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Guo J, Sun G, Zhao B, Wang L, Hong W, Sidorov VA, Ma N, Wu Q, Li S, Meng ZY, Sandvik AW, Sun L. Quantum Phases of SrCu_{2}(BO_{3})_{2} from High-Pressure Thermodynamics. PHYSICAL REVIEW LETTERS 2020; 124:206602. [PMID: 32501105 DOI: 10.1103/physrevlett.124.206602] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2019] [Accepted: 04/23/2020] [Indexed: 06/11/2023]
Abstract
We report heat capacity measurements of SrCu_{2}(BO_{3})_{2} under high pressure along with simulations of relevant quantum spin models and map out the (P,T) phase diagram of the material. We find a first-order quantum phase transition between the low-pressure quantum dimer paramagnet and a phase with signatures of a plaquette-singlet state below T=2 K. At higher pressures, we observe a transition into a previously unknown antiferromagnetic state below 4 K. Our findings can be explained within the two-dimensional Shastry-Sutherland quantum spin model supplemented by weak interlayer couplings. The possibility to tune SrCu_{2}(BO_{3})_{2} between the plaquette-singlet and antiferromagnetic states opens opportunities for experimental tests of quantum field theories and lattice models involving fractionalized excitations, emergent symmetries, and gauge fluctuations.
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Affiliation(s)
- Jing Guo
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Guangyu Sun
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Bowen Zhao
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Ling Wang
- Beijing Computational Science Research Center, 10 East Xibeiwang Road, Beijing 100193, China
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China
| | - Wenshan Hong
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Vladimir A Sidorov
- Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - Nvsen Ma
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Qi Wu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Shiliang Li
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Zi Yang Meng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Anders W Sandvik
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Liling Sun
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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Wang L, Sandvik AW. Critical Level Crossings and Gapless Spin Liquid in the Square-Lattice Spin-1/2 J_{1}-J_{2} Heisenberg Antiferromagnet. PHYSICAL REVIEW LETTERS 2018; 121:107202. [PMID: 30240235 DOI: 10.1103/physrevlett.121.107202] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2017] [Indexed: 06/08/2023]
Abstract
We use the density matrix renormalization group method to calculate several energy eigenvalues of the frustrated S=1/2 square-lattice J_{1}-J_{2} Heisenberg model on 2L×L cylinders with L≤10. We identify excited-level crossings versus the coupling ratio g=J_{2}/J_{1} and study their drifts with the system size L. The lowest singlet-triplet and singlet-quintuplet crossings converge rapidly (with corrections ∝L^{-2}) to different g values, and we argue that these correspond to ground-state transitions between the Néel antiferromagnet and a gapless spin liquid, at g_{c1}≈0.46, and between the spin liquid and a valence-bond solid at g_{c2}≈0.52. Previous studies of order parameters were not able to positively discriminate between an extended spin liquid phase and a critical point. We expect level-crossing analysis to be a generically powerful tool in density matrix renormalization group studies of quantum phase transitions.
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Affiliation(s)
- Ling Wang
- Beijing Computational Science Research Center, 10 East Xibeiwang Road, Beijing 100193, China
| | - Anders W Sandvik
- Beijing Computational Science Research Center, 10 East Xibeiwang Road, Beijing 100193, China
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Beijing National Laboratory of Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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7
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Plekhanov K, Vasić I, Petrescu A, Nirwan R, Roux G, Hofstetter W, Le Hur K. Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model. PHYSICAL REVIEW LETTERS 2018; 120:157201. [PMID: 29756857 DOI: 10.1103/physrevlett.120.157201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2017] [Revised: 11/13/2017] [Indexed: 06/08/2023]
Abstract
Recently, the frustrated XY model for spins 1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultracold atom setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using bosonic dynamical mean-field theory. Focusing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).
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Affiliation(s)
- Kirill Plekhanov
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
- Centre de Physique Théorique, Ecole Polytechnique, CNRS, Université Paris-Saclay, F-91128 Palaiseau, France
| | - Ivana Vasić
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, 11080 Belgrade, Serbia
| | - Alexandru Petrescu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Rajbir Nirwan
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt/Main, Germany
| | - Guillaume Roux
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Walter Hofstetter
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt/Main, Germany
| | - Karyn Le Hur
- Centre de Physique Théorique, Ecole Polytechnique, CNRS, Université Paris-Saclay, F-91128 Palaiseau, France
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8
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Nishimoto S, Katukuri VM, Yushankhai V, Stoll H, Rößler UK, Hozoi L, Rousochatzakis I, van den Brink J. Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3. Nat Commun 2016; 7:10273. [PMID: 26776664 PMCID: PMC4735606 DOI: 10.1038/ncomms10273] [Citation(s) in RCA: 61] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2014] [Accepted: 11/24/2015] [Indexed: 11/09/2022] Open
Abstract
Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir(4+) in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir-Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.
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Affiliation(s)
- Satoshi Nishimoto
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Vamshi M Katukuri
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Viktor Yushankhai
- Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Russia.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Street 38, 01187 Dresden, Germany
| | - Hermann Stoll
- Institute for Theoretical Chemistry, Universität Stuttgart, Pfaffenwaldring 55, 70550 Stuttgart, Germany
| | - Ulrich K Rößler
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Liviu Hozoi
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Ioannis Rousochatzakis
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Street 38, 01187 Dresden, Germany
| | - Jeroen van den Brink
- Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany.,Department of Physics, Technical University Dresden, Helmholtzstrasse 10, 01069 Dresden, Germany
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9
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Liu W, Wang C, Li Y, Lao Y, Han Y, Guo GC, Zhao YH, He L. Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:085601. [PMID: 25654245 DOI: 10.1088/0953-8984/27/8/085601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Tensor network states (TNS) methods combined with the Monte Carlo (MC) technique have been proven a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling technique, by mapping the energy function of the TNS to that of a classical mechanical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg J1-J2 model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.
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Affiliation(s)
- Wenyuan Liu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China. Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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10
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Weisse A. Divide and conquer the Hilbert space of translation-symmetric spin systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:043305. [PMID: 23679546 DOI: 10.1103/physreve.87.043305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2012] [Indexed: 06/02/2023]
Abstract
Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. To reach sensible system sizes such numerical calculations heavily depend on the use of symmetries. We describe a divide-and-conquer strategy for implementing translation symmetries of finite spin clusters, which efficiently uses and extends the "sublattice coding" of H. Q. Lin [Phys. Rev. B 42, 6561 (1990)]. With our method, the Hamiltonian matrix can be generated on-the-fly in each matrix vector multiplication, and problem dimensions beyond 10^{11} become accessible.
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Affiliation(s)
- Alexander Weisse
- Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany.
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11
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Kaul RK, Sandvik AW. Lattice model for the SU(N) Néel to valence-bond solid quantum phase transition at large N. PHYSICAL REVIEW LETTERS 2012; 108:137201. [PMID: 22540722 DOI: 10.1103/physrevlett.108.137201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2011] [Indexed: 05/31/2023]
Abstract
We generalize the SU(N=2) S=1/2 square-lattice quantum magnet with nearest-neighbor antiferromagnetic coupling (J(1)) and next-nearest-neighbor ferromagnetic coupling (J(2)) to arbitrary N. For all N>4, the ground state has valence-bond-solid order for J(2)=0 and Néel order for J(2)/J(1)≫1, allowing us access to the transition between these types of states for large N. Using quantum Monte Carlo simulations, we show that both order parameters vanish at a single quantum-critical point, whose universal exponents for large enough N (here up to N=12) approach the values obtained in a 1/N expansion of the noncompact CP(N-1) field theory. These results lend strong support to the deconfined quantum-criticality theory of the Néel-valence-bond-solid transition.
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Affiliation(s)
- Ribhu K Kaul
- Department of Physics & Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055, USA
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12
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Chen CC, Jia CJ, Kemper AF, Singh RRP, Devereaux TP. Theory of two-magnon Raman scattering in iron pnictides and chalcogenides. PHYSICAL REVIEW LETTERS 2011; 106:067002. [PMID: 21405486 DOI: 10.1103/physrevlett.106.067002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2010] [Indexed: 05/30/2023]
Abstract
Although the parent iron-based pnictides and chalcogenides are itinerant antiferromagnets, the use of local moment picture to understand their magnetic properties is still widespread. We study magnetic Raman scattering from a local moment perspective for various quantum spin models proposed for this new class of superconductors. These models vary greatly in the level of magnetic frustration and show a vastly different two-magnon Raman response. Light scattering by two-magnon excitations thus provides a robust and independent measure of the underlying spin interactions. In accord with other recent experiments, our results indicate that the amount of magnetic frustration in these systems may be small.
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Affiliation(s)
- C-C Chen
- Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
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13
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Becca F, Capriotti L, Parola A, Sorella S. Variational Wave Functions for Frustrated Magnetic Models. INTRODUCTION TO FRUSTRATED MAGNETISM 2011. [DOI: 10.1007/978-3-642-10589-0_15] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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14
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Schnalle R, Schnack J. Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries. INT REV PHYS CHEM 2010. [DOI: 10.1080/0144235x.2010.485755] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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15
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Sandvik AW. Continuous quantum phase transition between an antiferromagnet and a valence-bond solid in two dimensions: evidence for logarithmic corrections to scaling. PHYSICAL REVIEW LETTERS 2010; 104:177201. [PMID: 20482133 DOI: 10.1103/physrevlett.104.177201] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2010] [Indexed: 05/29/2023]
Abstract
The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S=1/2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations. The results support a continuous transition of the ground state, in agreement with the theory of "deconfined" quantum criticality. There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated. This suggests that either the SU(N) symmetric noncompact CP;{N-1} field theory for deconfined quantum criticality has to be revised or that the theory for N=2 (as in the system studied here) differs significantly from N-->infinity (where the field theory is analytically tractable).
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Affiliation(s)
- Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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16
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Liu CW, Liu S, Kao YJ, Chernyshev AL, Sandvik AW. Impurity-induced frustration in correlated oxides. PHYSICAL REVIEW LETTERS 2009; 102:167201. [PMID: 19518748 DOI: 10.1103/physrevlett.102.167201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2008] [Revised: 02/24/2009] [Indexed: 05/27/2023]
Abstract
Using the example of Zn-doped La2CuO4, we demonstrate that a spinless impurity doped into a nonfrustrated antiferromagnet can induce substantial frustrating interactions among the spins surrounding it. This result is the key to resolving discrepancies between experimental data and earlier theories. Analytic and quantum Monte Carlo studies of the impurity-induced frustration are in a close accord with each other and experiments. The proposed mechanism should be common to other correlated oxides.
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Affiliation(s)
- Cheng-Wei Liu
- Department of Physics, National Taiwan University, Taipei, Taiwan 106
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17
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Simulations of pure and doped low-dimensional spin-1/2 gapped systems. ACTA ACUST UNITED AC 2008. [DOI: 10.1007/bfb0119595] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/09/2023]
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18
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Sandvik AW. Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions. PHYSICAL REVIEW LETTERS 2007; 98:227202. [PMID: 17677875 DOI: 10.1103/physrevlett.98.227202] [Citation(s) in RCA: 88] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2006] [Indexed: 05/16/2023]
Abstract
Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.
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Affiliation(s)
- Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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19
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Schmalfuss D, Darradi R, Richter J, Schulenburg J, Ihle D. Quantum J1-J2 antiferromagnet on a stacked square lattice: influence of the interlayer coupling on the ground-state magnetic ordering. PHYSICAL REVIEW LETTERS 2006; 97:157201. [PMID: 17155352 DOI: 10.1103/physrevlett.97.157201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2006] [Indexed: 05/12/2023]
Abstract
Using the coupled-cluster method and the rotation-invariant Green's function method, we study the influence of the interlayer coupling Jperpendicular on the magnetic ordering in the ground state of the spin-1/2 J1-J2 frustrated Heisenberg antiferromagnet (J1-J2 model) on the stacked square lattice. In agreement with known results for the J1-J2 model on the strictly two-dimensional square lattice (Jperpendicular=0), we find that the phases with magnetic long-range order at small J2<Jc1 and large J2>Jc2 are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling Jperpendicular >0, the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small Jperpendicular approximately (0.2-0.3)J1.
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Affiliation(s)
- D Schmalfuss
- Institut für Theoretische Physik, Universität Magdeburg, 39016 Magdeburg, Germany
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Bombardi A, Rodriguez-Carvajal J, Di Matteo S, de Bergevin F, Paolasini L, Carretta P, Millet P, Caciuffo R. Direct determination of the magnetic ground state in the square lattice S = 1/2 antiferromagnet Li2VOSiO4. PHYSICAL REVIEW LETTERS 2004; 93:027202. [PMID: 15323947 DOI: 10.1103/physrevlett.93.027202] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2003] [Indexed: 05/24/2023]
Abstract
Powder neutron diffraction and resonant x-ray scattering measurements from a single crystal have been performed to study the low-temperature state of the 2D frustrated, quantum-Heisenberg system Li2VOSiO4. Both techniques indicate a collinear antiferromagnetic ground state, with propagation vector k=(1 / 2 1 / 2 0), and magnetic moments in the a-b plane. Contrary to previous reports, the ordered moment at 1.44 K, m=0.63(3)micro(B), is very close to the value expected for the square lattice Heisenberg model ( approximately 0.6micro(B)). The magnetic order is three dimensional, with antiferromagnetic a-b layers stacked ferromagnetically along the c axis. Neither x-ray nor neutron diffraction shows evidence for a structural distortion between 1.6 and 10 K.
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Affiliation(s)
- A Bombardi
- European Synchrotron Radiation Facility, BP 220, 38043 Grenoble, France
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Läuchli A, Poilblanc D. Spin-charge separation in two-dimensional frustrated quantum magnets. PHYSICAL REVIEW LETTERS 2004; 92:236404. [PMID: 15245179 DOI: 10.1103/physrevlett.92.236404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2003] [Indexed: 05/24/2023]
Abstract
The dynamics of a mobile hole in two-dimensional frustrated quantum magnets is investigated by exact diagonalization techniques. Our results provide evidence for spin-charge separation upon doping the kagome lattice, a prototype of a spin liquid. In contrast, in the checkerboard lattice, a symmetry broken valence bond crystal, a small quasiparticle peak is seen for some crystal momenta, a finding interpreted as a restoration of weak holon-spinon confinement.
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Affiliation(s)
- Andreas Läuchli
- Laboratoire de Physique Théorique, CNRS-UMR 5152, Université Paul Sabatier, F-31062 Toulouse, France
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Takano K, Kito Y, Ono Y, Sano K. Nonlinear sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry. PHYSICAL REVIEW LETTERS 2003; 91:197202. [PMID: 14611608 DOI: 10.1103/physrevlett.91.197202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2003] [Indexed: 05/24/2023]
Abstract
A novel nonlinear sigma model method is proposed for the two-dimensional J1-J2 model, which is extended to include plaquette-type distortion. The nonlinear sigma model is properly derived without spoiling the original spin degrees of freedom. The method shows that a single disordered phase continuously extends from a frustrated uniform regime to an unfrustrated distorted regime. By the continuity and Oshikawa's commensurability condition, the disordered ground states for the uniform J1-J2 model are plaquette states with fourfold degeneracy.
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Affiliation(s)
- Ken'ichi Takano
- Toyota Technological Institute, Tenpaku-ku, Nagoya 468-8511, Japan
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Carretta P, Melzi R, Papinutto N, Millet P. Very-low-frequency excitations in frustrated two-dimensional S = 1/2 Heisenberg antiferromagnets. PHYSICAL REVIEW LETTERS 2002; 88:047601. [PMID: 11801167 DOI: 10.1103/physrevlett.88.047601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2001] [Indexed: 05/23/2023]
Abstract
Muon spin resonance and 7Li NMR relaxation measurements in frustrated two-dimensional S = 1/2 Heisenberg antiferromagnets on a square lattice are presented. It is found that, in both Li2VOSiO4 and Li2VOGeO4, spin dynamics at frequencies orders of magnitude below the Heisenberg exchange frequency are present. These dynamics are associated with the motions of walls separating coexisting collinear domains with a magnetic wave vector rotated by 90 degrees.
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Affiliation(s)
- P Carretta
- Dipartimento di Fisica A. Volta e Unitá INFM di Pavia, Via Bassi 6, 27100 Pavia, Italy.
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Oitmaa J, Sushkov OP. Two-dimensional randomly frustrated spin-1/2 Heisenberg model. PHYSICAL REVIEW LETTERS 2001; 87:167206. [PMID: 11690241 DOI: 10.1103/physrevlett.87.167206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2001] [Indexed: 05/23/2023]
Abstract
We investigate the properties of S = 1/2 Heisenberg clusters with random frustration using exact diagonalizations. This is a model for a quantum spin glass. We show that the average ground state spin is S proportional to the square root of N, where N is the number of sites. We also calculate the magnetic susceptibility and the spin stiffness and low-energy excitations and discuss these in terms of a semiclassical picture.
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Affiliation(s)
- J Oitmaa
- School of Physics, University of New South Wales, Sydney 2052, Australia
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Bignonneau G, Fritsch A, Ducasse L. Non-orthogonal orbitals for localized electrons III. Application to periodic one dimensional lattices. Chem Phys 2001. [DOI: 10.1016/s0301-0104(01)00316-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Melzi R, Carretta P, Lascialfari A, Mambrini M, Troyer M, Millet P, Mila F. Li2VO(Si,Ge)O4, a prototype of a two-dimensional frustrated quantum heisenberg antiferromagnet. PHYSICAL REVIEW LETTERS 2000; 85:1318-1321. [PMID: 10991541 DOI: 10.1103/physrevlett.85.1318] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2000] [Indexed: 05/23/2023]
Abstract
NMR and magnetization measurements in Li2VOSiO4 and Li2VOGeO4 are reported. The analysis of the susceptibility shows that both compounds are two-dimensional S = 1/2 Heisenberg antiferromagnets on a square lattice with a sizable frustration induced by the competition between the superexchange couplings J1 along the sides of the square and J2 along the diagonal. Li2VOSiO4 undergoes a low-temperature phase transition to a collinear order, as theoretically predicted for J2/J1>0.5. Just above the magnetic transition the degeneracy between the two collinear ground states is lifted by the onset of a structural distortion.
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Affiliation(s)
- R Melzi
- Dipartimento di Fisica "A. Volta," Unita INFM di Pavia, 27100 Pavia, Italy
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Capriotti L, Sorella S. Spontaneous plaquette dimerization in the J1-J2 heisenberg model. PHYSICAL REVIEW LETTERS 2000; 84:3173-3176. [PMID: 11019040 DOI: 10.1103/physrevlett.84.3173] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/1999] [Indexed: 05/23/2023]
Abstract
We investigate the nonmagnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected "plaquette resonating valence bond," with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for J(2)/J(1) approximately 0.5.
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Affiliation(s)
- L Capriotti
- Istituto Nazionale di Fisica della Materia and International School for Advanced Studies, Via Beirut 4, I-34013 Trieste, Italy
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Hamer CJ, Hövelborn T, Bachhuber M. Finite-size scaling in the spin- model on a square lattice. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/32/1/007] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Chandra S, Malhotra LK, Dhara S, Rastogi AC. Low-temperature dynamic susceptibility of thin Cd1-xMnxTe films. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:13694-13704. [PMID: 9985284 DOI: 10.1103/physrevb.54.13694] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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