On The Entanglement Entropy For Gauge Theories

TL;DR

This paper introduces a new, lattice-based definition of entanglement entropy for gauge theories that aligns with existing methods like the replica trick but differs from entanglement distillation measures.

Contribution

It provides a unified entanglement entropy definition applicable to both Abelian and Non-Abelian gauge theories on a lattice.

Findings

The definition agrees with Casini, Huerta, and Rosabal's for certain cases.

It matches the replica trick calculations in general.

It differs from entanglement distillation measures.

Abstract

We propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For $\mathbb{Z}_N$ and $U(1)$ theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglement entropy calculated using a definition of the replica trick. Our definition, however, does not agree with some standard ways to measure entanglement, like the number of Bell pairs which can be produced by entanglement distillation.