Building Projected Entangled Pair States with a Local Gauge Symmetry

TL;DR

This paper introduces a framework for constructing gauge-invariant PEPS that can represent both bosonic and fermionic states in lattice gauge theories, aiding theoretical analysis and quantum simulation.

Contribution

It presents a novel method for building PEPS with local gauge symmetry applicable to various matter and gauge field combinations in lattice gauge theories.

Findings

Framework for gauge-invariant PEPS including bosonic and fermionic states

Applicable to theories with finite or compact Lie groups

Facilitates analysis and simulation of lattice gauge theories

Abstract

Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.