Symmetry-projected cluster mean-field theory applied to spin systems

Abstract

We introduce $S_z$ spin-projection based on cluster mean-field theory and apply it to the ground state of strongly-correlated spin systems. In cluster mean-field, 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 $S_z$ symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all $S_z$ sectors, breaking $S_z$ symmetry. In addition, a projection scheme is used to restore global $S_z$, which gives rise to $S_z$ spin-projected generalized cluster mean-field (S${}_z$GcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D $J_1-J_2$ and $XXZ$ Heisenberg models. Our results indicate that the new methods (GcMF and S${}_z$GcMF) 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.

References in corpus (59)

• The ITensor Software Library for Tensor Network Calculations
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Low-energy spectrum of iron-sulfur clusters directly from many-particle quantum mechanics
• A practical guide to density matrix embedding theory in quantum chemistry
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Projected Hartree-Fock Theory
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Exactly-embedded multiconfigurational self-consistent field theory using density matrix embedding: the localized active space self-consistent field method
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Phase Transitions in the Spin-Half J_1--J_2 Model
• Projected Coupled Cluster Theory
• Selected Configuration Interaction in a Basis of Cluster State Tensor Products
• Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry
• Gapped spin liquid phase in the J1-J2 Heisenberg model by a Bosonic resonating valence-bond ansatz
• Symmetry-projected Wave Functions in Quantum Monte Carlo Calculations
• Multi-component symmetry-projected approach for molecular ground state correlations
• Multi-reference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model
• A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
• Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model
• Correlating the Antisymmetrized Geminal Power Wave Function
• Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
• Describing Strong Correlation with Block-Correlated Coupled Cluster Theory
• Exploring non-linear correlators on AGP
• Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures
• Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration
• High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
• Projected Hartree-Fock as a Polynomial of Particle-Hole Excitations and Its Combination With Variational Coupled Cluster Theory
• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• The Ising phase in the J1-J2 Heisenberg Model
• Projected Coupled Cluster Theory: Optimization of cluster amplitudes in the presence of symmetry projection
• Guide to Exact Diagonalization Study of Quantum Thermalization
• Hartree-Fock symmetry breaking around conical intersections
• Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants
• Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model
• Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations
• Colorful points in the XY regime of XXZ quantum magnets
• Attenuated Coupled Cluster: A Heuristic Polynomial Similarity Transformation Incorporating Spin Symmetry Projection Into Traditional Coupled Cluster Theory
• Exploring Spin AGP Ansatze for Strongly Correlated Spin Systems
• Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model
• A Power Series Approximation in Symmetry Projected Coupled Cluster Theory
• Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory
• Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach

Cited by in corpus (4)

• Linear combinations of cluster mean-field states applied to spin systems
• Efficient simulation of inhomogeneously correlated systems using block interaction product states
• Projective spin adaptation for the exact diagonalization of isotropic spin clusters
• Symmetry-Projected Spin-AGP Methods Applied to Spin Systems