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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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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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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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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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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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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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Nunes WA, de Sousa JR, Viana JR, Richter J. The quantum spin-1/2 J1-J2 antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:146004. [PMID: 21389538 DOI: 10.1088/0953-8984/22/14/146004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The ground state phase diagram of the quantum spin-1/2 Heisenberg antiferromagnet in the presence of nearest-neighbor (J(1)) and next-nearest-neighbor (J(2)) interactions (J(1)-J(2) model) on a stacked square lattice, where we introduce an interlayer coupling through nearest-neighbor bonds of strength J(<perpendicular>), is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in a cluster with N=4 spins (EFT-4). We obtain the sublattice magnetization m(A) for the ordered phases: antiferromagnetic (AF) and collinear (CAF-collinear antiferromagnetic). We propose a functional for the free energy Ψ(μ)(m(μ)) (μ=A, B) to obtain the phase diagram in the λ-α plane, where λ=J(<perpendicular>)/J(1) and α=J(2)/J(1). Depending on the values of λ and α, we found different ordered states (AF and CAF) and a disordered state (quantum paramagnetic (QP)). For an intermediate region α(1c)(λ) < α < α(2c)(λ) we observe a QP phase that disappears for λ below some critical value λ(1)≈0.67. For α < α(1c)(λ) and α > α(2c)(λ), and below λ(1), we have the AF and CAF semi-classically ordered states, respectively. At α=α(1c)(λ) a second-order transition between the AF and QP states occurs and at α=α(2c)(λ) a first-order transition between the AF and CAF phases takes place. The boundaries between these ordered phases merge at the critical end point CEP≡(λ(1), α(c)), where α(c)≈0.56. Above this CEP there is again a direct first-order transition between the AF and CAF phases, with a behavior described by the point α(c) independent of λ ≥ λ(1).
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Affiliation(s)
- Wagner A Nunes
- Departamento de Física, Universidade Federal do Amazonas, 3000, Japiim, 69077-000, Manaus-AM, Brazil
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