Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo

Abstract

We propose a new ansatz for the ground-state wave function of quantum many-body systems on a lattice. The key idea is to cover the lattice with plaquettes and obtain a state whose configurational weights can be optimized by means of a Variational Monte Carlo algorithm. Such a scheme applies to any dimension, without any "sign" instability. We show results for various two dimensional spin models (including frustrated ones). A detailed comparison with available exact results, as well as with variational methods based on different ansatzs is offered. In particular, our numerical estimates are in quite good agreement with exact ones for unfrustrated systems, and compare favorably to other methods for frustrated ones.

5 pages, 2 figures (see also arXiv:0907.4646)

References in corpus (9)

• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Entropy and Entanglement in Quantum Ground States
• Variational quantum Monte Carlo simulations with tensor-network states
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice

Cited by in corpus (79)

• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• The density matrix renormalization group for ab initio quantum chemistry
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Algorithms for finite Projected Entangled Pair States
• Tensor factorizations of local second-order Møller Plesset theory
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Nature of the spin liquid state of the Hubbard model on honeycomb lattice
• Optimizing large parameter sets in variational quantum Monte Carlo
• Approximating strongly correlated spin and fermion wavefunctions with correlator product states
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• Linear-scaling and parallelizable algorithms for stochastic quantum chemistry
• Solving frustrated quantum many-particle models with convolutional neural networks
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• An exactly size consistent geminal power via Jastrow factor networks in a local one particle basis
• Ground-state phase diagram of the quantum J1-J2 model on the honeycomb lattice
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• The Variational Power of Quantum Circuit Tensor Networks
• Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
• Neural network wave functions and the sign problem
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations
• A Jastrow factor coupled cluster theory for weak and strong electron correlation
• Higher order tensor renormalization group for relativistic fermion systems
• A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
• Interaction-induced anomalous quantum Hall state on the honeycomb lattice
• Solving condensed-matter ground-state problems by semidefinite relaxations
• Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states
• Conversion of projected entangled pair states into a canonical form
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• A Projector Quantum Monte Carlo Method for non-linear wavefunctions
• Simulating two- and three-dimensional frustrated quantum systems with string-bond states
• Categorical Tensor Network States
• Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice: A variational study based on entangled-plaquette states
• Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
• Further developments in correlator product states: deterministic optimization and energy evaluation
• The area law and real-space renormalization
• Differences in the quasiparticle dynamics for one-band and three-band cuprate models
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Projector quantum Monte Carlo with matrix product states
• Complementary First and Second Derivative Methods for Ansatz Optimization in Variational Monte Carlo
• Automatic Differentiable Monte Carlo: Theory and Application
• Long-Range Entangled-Plaquette States for Critical and Frustrated Quantum Systems on a Lattice
• Finite temperature properties of strongly correlated systems via variational Monte Carlo
• Fermi Arcs From Dynamical Variational Monte Carlo
• Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz
• Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
• An accelerated linear method for optimizing non-linear wavefunctions in variational Monte Carlo
• A correlator product state study of molecular magnetism in the giant Keplerate Mo72Fe30
• Variational Monte Carlo simulations using tensor-product projected states
• Gaussian Process States: A data-driven representation of quantum many-body physics
• Efficient representation of long-range interactions in tensor network algorithms
• Unifying view of fermionic neural network quantum states: From neural network backflow to hidden fermion determinant states
• Benchmarking the variational reduced density matrix theory in the doubly-occupied configuration interaction space with integrable pairing models
• Matrix Product States with Backflow correlations
• Variational study of a mobile hole in a two dimensional quantum antiferromagnet using entangled-plaquette states
• Matrix-Product based Projected Wave Functions Ansatz for Quantum Many-Body Ground States
• Self-Adaptive Tensor Network States with Multi-Site Correlators
• Certifying ground-state properties of quantum many-body systems
• The quantum Gaussian process state: A kernel-inspired state with quantum support data
• A framework for efficient ab initio electronic structure with Gaussian Process States
• Two holes in a two-dimensional quantum antiferromagnet: A variational study based on entangled-plaquette states
• Drude and Superconducting Weights and Mott Transitions in Variation Theory
• Efficient neural-network based variational Monte Carlo scheme for direct optimization of excited energy states in frustrated quantum systems
• Strongly Interacting Two-component Coupled Bose Gas in Optical Lattices
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Tensor Network States with Three-Site Correlators
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Boltzmann machines and quantum many-body problems
• Machine Learning Wavefunction
• Variational Neural and Tensor Network Approximations of Thermal States
• Time Evolution and Deterministic Optimisation of Correlator Product States
• Computational scheme for the spin-1/2 square lattice Heisenberg antiferromagnet based on an octapartite description of the square lattice
• Improving neural network performance for solving quantum sign structure