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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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Wieser R. Investigation of the temperature phase diagram of the 2D semi-classical ferrimagneticJ1-J2model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:395802. [PMID: 35856844 DOI: 10.1088/1361-648x/ac829f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2022] [Accepted: 07/20/2022] [Indexed: 06/15/2023]
Abstract
The temperature phase diagram (ToverJ2) of the 2D semiclassicalJ1-J2Heisenberg model is discussed. The investigation was carried out using the self-consistent Bloch equation and a quantum statistical description of the magnetization. In addition to the three states of the zero-temperature phase diagram, theJ2-Tphase diagram shows two new phases, the paramagnetic phase and the semi-paramagneticS1-Néel state. The five occurring ground states, as well as the transitions between these states, are discussed. In particular, attention is paid to the interplay between temperature and frustration.
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Affiliation(s)
- R Wieser
- School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, People's Republic of China
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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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5
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Gapless quantum spin liquid and global phase diagram of the spin-1/2 J1-J2 square antiferromagnetic Heisenberg model. Sci Bull (Beijing) 2022; 67:1034-1041. [DOI: 10.1016/j.scib.2022.03.010] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Revised: 02/27/2022] [Accepted: 03/07/2022] [Indexed: 11/16/2022]
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6
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Wieser R. Investigation of the magnetic phase diagram of the 2D ferrimagnetic J 1-J 2 model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:095901. [PMID: 33319771 DOI: 10.1088/1361-648x/abcbda] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The zero-temperature phase diagram and spin dynamics of the 2D ferrimagnetic J 1-J 2 model with (S 1, S 2) = (1/2, 1) are investigated using the time-dependent cluster mean-field theory (t-CMFT). The t-CMFT enables the investigation of the quantum-mechanical as well as semi-classical phase diagram and spin dynamics by control of the entanglement. For the characterization of the ferrimagnetic system, the magnetization, the energy per atom, the cluster quantum states and the von Neumann entropy have been determined.
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Affiliation(s)
- R Wieser
- School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, People's Republic of China
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7
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Lidiak A, Gong Z. Unsupervised Machine Learning of Quantum Phase Transitions Using Diffusion Maps. PHYSICAL REVIEW LETTERS 2020; 125:225701. [PMID: 33315426 DOI: 10.1103/physrevlett.125.225701] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 10/15/2020] [Indexed: 06/12/2023]
Abstract
Experimental quantum simulators have become large and complex enough that discovering new physics from the huge amount of measurement data can be quite challenging, especially when little theoretical understanding of the simulated model is available. Unsupervised machine learning methods are particularly promising in overcoming this challenge. For the specific task of learning quantum phase transitions, unsupervised machine learning methods have primarily been developed for phase transitions characterized by simple order parameters, typically linear in the measured observables. However, such methods often fail for more complicated phase transitions, such as those involving incommensurate phases, valence-bond solids, topological order, and many-body localization. We show that the diffusion map method, which performs nonlinear dimensionality reduction and spectral clustering of the measurement data, has significant potential for learning such complex phase transitions unsupervised. This method may work for measurements of local observables in a single basis and is thus readily applicable to many experimental quantum simulators as a versatile tool for learning various quantum phases and phase transitions.
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Affiliation(s)
- Alexander Lidiak
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Zhexuan Gong
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
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8
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Deb M, Ghosh AK. Exotic topological point and line nodes in the plaquette excitations of a frustrated Heisenberg antiferromagnet on the honeycomb lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:365601. [PMID: 32240991 DOI: 10.1088/1361-648x/ab85f7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 04/02/2020] [Indexed: 06/11/2023]
Abstract
A number of topological nodes including Dirac, quadratic and three-band touching points as well as a pair of degenerate Dirac line nodes are found to emerge in the triplet plaquette excitations of the frustrated spin-1/2J1-J2antiferromagnetic Heisenberg honeycomb model when the ground state of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A six-spin plaquette operator theory of this honeycomb model has been developed for this purpose by using the eigenstates of an isolated Heisenberg hexagonal plaquette. Spin-1/2 operators are thus expressed in the Fock space spanned by the plaquette operators those are obtained in terms of exact analytic form of eigenstates for a single frustrated Heisenberg hexagon. Ultimately, an effective interacting boson model of this system is obtained on the basis of low energy singlets and triplets plaquette operators by employing a mean-field approximation. The values of ground state energy and spin gap of this system have been estimated and the validity of this formalism has been tested upon comparison with the known results. Emergence of topological point and line nodes on the basis of spin-disordered ground state noted in this investigation is very rare on any frustrated system as well as the presence of triplet flat band. Evolution of those topological nodes is studied throughout the full frustrated regime. Finally, emergence of topological phases has been reported upon adding a time-reversal-symmetry breaking term to the Hamiltonian. Coexistence of spin gap with either topological nodes or phases turns this honeycomb model an interesting one.
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Affiliation(s)
- Moumita Deb
- Department of Physics, Jadavpur University, 188 Raja Subodh Chandra Mallik Road, Kolkata 700032, India
| | - Asim Kumar Ghosh
- Department of Physics, Jadavpur University, 188 Raja Subodh Chandra Mallik Road, Kolkata 700032, India
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9
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Mustonen O, Vasala S, Sadrollahi E, Schmidt KP, Baines C, Walker HC, Terasaki I, Litterst FJ, Baggio-Saitovitch E, Karppinen M. Spin-liquid-like state in a spin-1/2 square-lattice antiferromagnet perovskite induced by d 10-d 0 cation mixing. Nat Commun 2018. [PMID: 29540711 PMCID: PMC5852160 DOI: 10.1038/s41467-018-03435-1] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Abstract
A quantum spin liquid state has long been predicted to arise in spin-1/2 Heisenberg square-lattice antiferromagnets at the boundary region between Néel (nearest-neighbor interaction dominates) and columnar (next-nearest-neighbor interaction dominates) antiferromagnetic order. However, there are no known compounds in this region. Here we use d10-d0 cation mixing to tune the magnetic interactions on the square lattice while simultaneously introducing disorder. We find spin-liquid-like behavior in the double perovskite Sr2Cu(Te0.5W0.5)O6, where the isostructural end phases Sr2CuTeO6 and Sr2CuWO6 are Néel and columnar type antiferromagnets, respectively. We show that magnetism in Sr2Cu(Te0.5W0.5)O6 is entirely dynamic down to 19 mK. Additionally, we observe at low temperatures for Sr2Cu(Te0.5W0.5)O6-similar to several spin liquid candidates-a plateau in muon spin relaxation rate and a strong T-linear dependence in specific heat. Our observations for Sr2Cu(Te0.5W0.5)O6 highlight the role of disorder in addition to magnetic frustration in spin liquid physics.
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Affiliation(s)
- O Mustonen
- Department of Chemistry and Materials Science, Aalto University, FI-00076, Espoo, Finland
| | - S Vasala
- Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr Xavier Sigaud 150, Urca, Rio de Janeiro, 22290-180, Brazil
| | - E Sadrollahi
- Institut für Physik der Kondensierten Materie, Technische Universität Braunschweig, 38110, Braunschweig, Germany
| | - K P Schmidt
- Institut für Physik der Kondensierten Materie, Technische Universität Braunschweig, 38110, Braunschweig, Germany
| | - C Baines
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, 5232, Villigen PSI, Switzerland
| | - H C Walker
- ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, UK
| | - I Terasaki
- Department of Physics, Nagoya University, Nagoya, 464-8602, Japan
| | - F J Litterst
- Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr Xavier Sigaud 150, Urca, Rio de Janeiro, 22290-180, Brazil.,Institut für Physik der Kondensierten Materie, Technische Universität Braunschweig, 38110, Braunschweig, Germany
| | - E Baggio-Saitovitch
- Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr Xavier Sigaud 150, Urca, Rio de Janeiro, 22290-180, Brazil
| | - M Karppinen
- Department of Chemistry and Materials Science, Aalto University, FI-00076, Espoo, Finland.
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10
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Rehn J, Sen A, Damle K, Moessner R. Classical Spin Liquid on the Maximally Frustrated Honeycomb Lattice. PHYSICAL REVIEW LETTERS 2016; 117:167201. [PMID: 27792369 DOI: 10.1103/physrevlett.117.167201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2015] [Indexed: 06/06/2023]
Abstract
We show that the honeycomb Heisenberg antiferromagnet with J_{1}/2=J_{2}=J_{3}, where J_{1}, J_{2}, and J_{3} are first-, second-, and third-neighbor couplings, respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with nonmagnetic ions, fractionalized degrees of freedom carrying 1/3 of the free moment emerge. Their effective description in the limit of low temperature is that of spins randomly located on a triangular lattice, with a frustrated sublattice-sensitive interaction of long-ranged logarithmic form. The XY version of this magnet exhibits nematic thermal order by disorder. This comes with a clear experimental diagnostic in neutron scattering, which turns out to apply also to the case of the celebrated planar order by disorder of the kagome Heisenberg antiferromagnet.
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Affiliation(s)
- J Rehn
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - Arnab Sen
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata 700032, India
| | - Kedar Damle
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400 005, India
| | - R Moessner
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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11
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Gong SS, Zhu W, Sheng DN, Motrunich OI, Fisher MPA. Plaquette ordered phase and quantum phase diagram in the spin-1/2 J(1)-J(2) square Heisenberg model. PHYSICAL REVIEW LETTERS 2014; 113:027201. [PMID: 25062223 DOI: 10.1103/physrevlett.113.027201] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2014] [Indexed: 06/03/2023]
Abstract
We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z(2) spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J(2), we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J(2)/J(1)≃0.44. For 0.5<J(2)/J(1)<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J(2)/J(1)<0.5, spin order, dimer order, and spin gap are small on finite-size systems, which is consistent with a near-critical behavior. The critical exponents obtained from the finite-size spin and dimer correlations could be compatible with the deconfined criticality in this small region. We compare and contrast our results with earlier numerical studies.
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Affiliation(s)
- Shou-Shu Gong
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Wei Zhu
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Olexei I Motrunich
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Matthew P A Fisher
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
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12
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Ren YZ, Tong NH, Xie XC. Cluster mean-field theory study of J1-J2 Heisenberg model on a square lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:115601. [PMID: 24589877 DOI: 10.1088/0953-8984/26/11/115601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study the spin-1/2 J1-J2 Heisenberg model on a square lattice using the cluster mean-field theory. We find a rapid convergence of phase boundaries with increasing cluster size. By extrapolating the cluster size L to infinity, we obtain accurate phase boundaries J(c1)(2) ≈ 0.42 (between the Néel antiferromagnetic phase and non-magnetic phase), and J(c2)(2) ≈ 0.59 (between non-magnetic phase and the collinear antiferromagnetic phase). Our results support the second-order phase transition at J(c1)(2) and the first-order one at J(c2)(2). For the spin-anisotropic J1-J2 model, we present its finite temperature phase diagram and demonstrate that the non-magnetic state is unstable towards the first-order phase transition under intermediate spin anisotropy.
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Affiliation(s)
- Yong-Zhi Ren
- Department of Physics, Renmin University of China, 100872 Beijing, People's Republic of China
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Mosadeq H, Shahbazi F, Jafari SA. Plaquette valence bond ordering in a J1-J2 Heisenberg antiferromagnet on a honeycomb lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:226006. [PMID: 21593556 DOI: 10.1088/0953-8984/23/22/226006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study an S = 1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J(1)-J(2) model), employing exact diagonalization in both the S(z) = 0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2 < J(2)/J(1) < 0.3, the NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as the plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidates for the ground state in the frustrated region. We provide a body of evidence in favor of plaquette valence bond ordering for 0.2 < J(2)/J(1) < 0.3. By further increasing the ratio J(2)/J(1), this state undergoes a transition to the staggered dimerized state.
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Affiliation(s)
- H Mosadeq
- Department of Physics, Isfahan University of Technology, Isfahan, Iran.
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14
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Kotov VN, Oitmaa J, Sushkov O, Weihong Z. Spontaneous dimer order, excitation spectrum and quantum-phase transitions in the J1-J2 Heisenberg model. ACTA ACUST UNITED AC 2009. [DOI: 10.1080/13642810008208579] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Valeri N. Kotov
- a Department of Physics , University of Florida , Gainesville , Florida 32611-8440 , USA
| | - Jaan Oitmaa
- b School of Physics , University of New South Wales , Sydney 2052 , Australia
| | - Oleg Sushkov
- b School of Physics , University of New South Wales , Sydney 2052 , Australia
| | - Zheng Weihong
- b School of Physics , University of New South Wales , Sydney 2052 , Australia
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15
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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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16
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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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17
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Zhang GM, Hu H, Yu L. Valence-bond spin-liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets. PHYSICAL REVIEW LETTERS 2003; 91:067201. [PMID: 12935105 DOI: 10.1103/physrevlett.91.067201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2003] [Indexed: 05/24/2023]
Abstract
Fermionic valence-bond approach in terms of SU(4) representation is proposed to describe the J1-J2 frustrated Heisenberg antiferromagnetic (AF) model on a bipartite square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence-bond spin-liquid state, interpolating the two different AF ordered states in the large J1 and large J2 limits, respectively. This novel spin-liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structure factor is predicted for momenta q=(0,0) and (pi,pi) in the strongly frustrated limit J(2)/J(1) approximately 1/2, which can be checked by neutron scattering experiments.
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Affiliation(s)
- Guang-Ming Zhang
- Center for Advanced Study, Tsinghua University, Beijing 100084, China
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18
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Becca F, Mila F. Peierls-like transition induced by frustration in a two-dimensional antiferromagnet. PHYSICAL REVIEW LETTERS 2002; 89:037204. [PMID: 12144417 DOI: 10.1103/physrevlett.89.037204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2002] [Indexed: 05/23/2023]
Abstract
We show that the introduction of frustration into the spin- 1/2 two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest-neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for Li(2)VOSiO(4), the first realization of that model, will be discussed.
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Affiliation(s)
- Federico Becca
- Institut de Physique Théorique, Université de Lausanne, CH-1015 Lausanne, Switzerland
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Capriotti L, Becca F, Parola A, Sorella S. Resonating valence bond wave functions for strongly frustrated spin systems. PHYSICAL REVIEW LETTERS 2001; 87:097201. [PMID: 11531593 DOI: 10.1103/physrevlett.87.097201] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2001] [Indexed: 05/23/2023]
Abstract
The resonating-valence-bond (RVB) theory for two-dimensional quantum antiferromagnets is shown to be the correct paradigm for large enough "quantum frustration." This scenario, proposed a long time ago but never confirmed by microscopic calculations, is strongly supported by a new type of variational wave function, which is extremely close to the exact ground state of the J(1)-J(2) Heisenberg model for 0.4 less than approximately J(2)/J(1) less than approximately 0.5. This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.
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Affiliation(s)
- L Capriotti
- Istituto Nazionale per la Fisica della Materia, Unità di Firenze, I-50125 Firenze, Italy
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Zaliznyak IA, Hill JP, Tranquada JM, Erwin R, Moritomo Y. Independent freezing of charge and spin dynamics in La1.5Sr0.5CoO4. PHYSICAL REVIEW LETTERS 2000; 85:4353-4356. [PMID: 11060636 DOI: 10.1103/physrevlett.85.4353] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2000] [Indexed: 05/23/2023]
Abstract
We present elastic and quasielastic neutron scattering measurements characterizing peculiar short-range charge-orbital and spin order in the layered perovskite material La1.5Sr0.5CoO4. We find that below T(c) approximately 750 K holes introduced by Sr doping lose mobility and enter a statically ordered charge glass phase with loosely correlated checkerboard arrangement of empty and occupied d(3z(2)-r(2)) orbitals ( Co3+ and Co2+). The dynamics of the resultant mixed spin system is governed by the anisotropic nature of the crystal-field Hamiltonian and the peculiar exchange pattern produced by the orbital order. It undergoes a spin freezing transition at a much lower temperature, T(s) less, similar30 K.
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Affiliation(s)
- IA Zaliznyak
- Department of Physics, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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Zhitomirsky ME, Honecker A, Petrenko OA. Field induced ordering in highly frustrated antiferromagnets. PHYSICAL REVIEW LETTERS 2000; 85:3269-3272. [PMID: 11019318 DOI: 10.1103/physrevlett.85.3269] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2000] [Indexed: 05/23/2023]
Abstract
We predict that an external field can induce a spin ordering in highly frustrated classical Heisenberg magnets. We find analytically stabilization of collinear states by thermal fluctuations at a one-third of the saturation field for kagome and garnet lattices and at a half of the saturation field for pyrochlore and frustrated square lattices. This effect is studied numerically for the frustrated square-lattice antiferromagnet by Monte Carlo simulations for classical spins and by exact diagonalization for S = 1/2. The field induced collinear states have a spin gap and produce magnetization plateaus.
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Affiliation(s)
- M E Zhitomirsky
- Theoretische Physik, ETH Hönggerberg, CH-8093 Zürich, Switzerland
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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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