# Projected entangled pair states for lattice gauge theories with dynamical fermions

## TL;DR

The paper introduces a new method for simulating lattice gauge theories with fermions using projected entangled pair states, avoiding computational issues like the sign problem.

## Contribution

The novel contribution is applying gauged Gaussian projected entangled pair states to lattice gauge theories with dynamical fermions.

## Key findings

- The method shows agreement with exact diagonalization results for small systems.
- The approach is computationally feasible for larger systems where exact solutions are not available.
- This technique avoids the sign problem and can be extended to higher dimensions and other gauge groups.

## 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 \documentclass[12pt]{minimal}
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\begin{document}$${{\mathbb{Z}}}_{2}$$\end{document}Z2 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.

Simulating quantum field theories presents a host of computational challenges, including the large dimensionality of the problem and numerical obstacles such as the sign problem. The authors demonstrate a technique that is able to address these challenges, and show results for a lattice gauge theory which includes matter.