Linear combinations of cluster mean-field states applied to spin systems
arXiv:2402.06760 · doi:10.1021/acs.jctc.4c00171
Abstract
We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field (cMF) states, and apply it to describe the ground state of strongly-correlated spin systems. In cluster mean-field theory, the ground state wavefunction 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 and Heisenberg models. Our findings highlight two key aspects. First, the method offers a semi-quantitative description of the regime of the 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.
References in corpus (46)
- The ITensor Software Library for Tensor Network Calculations
- Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
- Spin Liquid Ground State of the Spin-1/2 Square - Heisenberg Model
- Low-energy spectrum of iron-sulfur clusters directly from many-particle quantum mechanics
- Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
- 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 spin liquid by frustrating Néel antiferromagnetism
- Spontaneous plaquette dimerization in the 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
- New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
- Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
- 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 -- antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
- Hierarchical mean-field approach to the - Heisenberg model on a square lattice
- Phase Transitions in the Spin-Half J_1--J_2 Model
- Selected Configuration Interaction in a Basis of Cluster State Tensor Products
- 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
- 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
- Exploring non-linear correlators on AGP
- Further developments in correlator product states: deterministic optimization and energy evaluation
- High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
- The Ising phase in the J1-J2 Heisenberg Model
- Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
- Guide to Exact Diagonalization Study of Quantum Thermalization
- Spin-Peierls vs. Peierls distortions in a family of conjugated Polymers
- Cluster many-body expansion: a many-body expansion of the electron correlation energy about a cluster mean-field reference
- 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- XXZ model
- Colorful points in the XY regime of XXZ quantum magnets
- Symmetry-projected cluster mean-field theory applied to spin systems
- 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
- Long-range spin-pairing order and spin defects in quantum spin-1/2 ladders
- Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach