Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories

TL;DR

This paper introduces a method combining tensor networks with Monte Carlo techniques to efficiently compute physical observables in lattice gauge theories, enabling studies in higher dimensions.

Contribution

It presents a novel approach that integrates tensor network states with Monte Carlo methods for lattice gauge theories, facilitating computations in 2D and 3D.

Findings

Efficient Monte Carlo computation of expectation values in tensor network states.

Potential to study complex lattice gauge theories in higher spatial dimensions.

Enables exploration of fermionic matter interacting with gauge fields.

Abstract

Gauged gaussian Projected Entangled Pair States are particular tensor network constructions that describe lattice states of fermionic matter interacting with dynamical gauge fields. We show how one can efficiently compute, using Monte-Carlo techniques, expectation values of physical observables in that class of states. This opens up the possibility of using tensor network techniques to investigate lattice gauge theories in two and three spatial dimensions.