Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions

TL;DR

This paper introduces gauged Gaussian projected entangled pair states as an ansatz for simulating lattice gauge theories with dynamical fermions, showing promising results for small and larger systems.

Contribution

It presents a novel tensor network approach for lattice gauge theories with dynamical matter, enabling studies beyond the reach of traditional Monte Carlo methods.

Findings

Results agree with exact diagonalization for small systems.

Approach is computationally feasible for larger systems.

Advances the study of higher-dimensional gauge theories without sign problems.

Abstract

Lattice gauge theory is an important framework for studying gauge theories that arise in the Standard Model and condensed matter physics. Yet many systems (or regimes of those systems) are difficult to study using conventional techniques, such as action-based Monte Carlo sampling. In this paper, we demonstrate the use of gauged Gaussian projected entangled pair states as an ansatz for a lattice gauge theory involving dynamical physical matter. We study a $\mathbb{Z}_2$ gauge theory on a two dimensional lattice with a single flavor of fermionic matter on each lattice site. For small systems, our results show agreement with results computed by exactly diagonalizing the Hamiltonian, and demonstrate that the approach is computationally feasible for larger system sizes where exact results are unavailable. This is a further step on the road to studying higher dimensions and other gauge groups with manageable computational costs while avoiding the sign problem.