Monte Carlo simulations of two-dimensional fermion systems with string-bond states

Abstract

We describe an application of variational Monte Carlo to two-dimensional fermionic systems within the recently developed tensor-network string-bond state (SBS) ansatz. We use a combination of variational Monte Carlo and stochastic optimization to optimize the matrix-product state matrices representing the ground state. We present results for a two-dimensional spinless fermion model including nearest-neighbor Coulomb interactions and determine using finite-size scaling the phase boundary between charge-ordered insulating and metallic phases. This approach can treat frustrated systems and be easily extended to for fermions with spin.

5 pages, 5 figures

References in corpus (19)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• The ALPS project release 1.3: open source software for strongly correlated systems
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Tensor renormalization group approach to 2D classical lattice models
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Renormalization of tensor-network states
• Variational quantum Monte Carlo simulations with tensor-network states
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• Monte Carlo simulation with Tensor Network States
• Real-Space Parallel Density Matrix Renormalization Group
• Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• Variational treatment of the Shastry-Sutherland antiferromagnet using Projected Entangled Pair States (PEPS)
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Ground state and finite temperature behavior of 1/4-filled band zigzag ladders

Cited by in corpus (8)

• Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states
• From charge- and spin-ordering to superconductivity in the organic charge-transfer solids
• Variational Monte Carlo simulations using tensor-product projected states
• Efficient neural-network based variational Monte Carlo scheme for direct optimization of excited energy states in frustrated quantum systems
• Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity
• Exotic Spin Phases in Two Dimensional Spin-orbit Coupled Models: Importance of Quantum Fluctuation Effects
• Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations
• Density Matrix Renormalization Group study of superconducting pairing near the quarter-filled Wigner crystal