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

TL;DR

This paper introduces a variational Monte Carlo method combined with tensor-network string-bond states to study two-dimensional fermionic systems, successfully identifying phase boundaries and demonstrating the approach's versatility.

Contribution

It presents a novel combination of variational Monte Carlo and string-bond tensor networks for 2D fermion systems, enabling efficient ground state optimization and phase diagram analysis.

Findings

Identified phase boundary between charge-ordered and metallic phases.

Demonstrated the method's applicability to frustrated systems.

Extended approach to fermions with spin.

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.