Notes on Entanglement in Abelian Gauge Theories

TL;DR

This paper presents a clear method for calculating entanglement entropy in Abelian gauge theories, resolving previous ambiguities and applicable to both lattice and continuum models with matter and continuous symmetries.

Contribution

It introduces an explicit prescription for entanglement entropy calculation in Abelian gauge theories, clarifying previous ambiguities and unifying various approaches.

Findings

The method applies to $ ext{Z}_N$ lattice gauge theories.

Previous calculations are special cases of the new setup.

Ambiguities are due to basis choices in gauge-invariant operators.

Abstract

We streamline and generalize the recent progress in understanding entanglement between spatial regions in Abelian gauge theories. We provide an unambiguous and explicit prescription for calculating entanglement entropy in a $\mathbb Z_N$ lattice gauge theory. The main idea is that the lattice should be split into two disjoint regions of links separated by a buffer zone of plaquettes. We show that the previous calculations of the entanglement entropy can be realized as special cases of our setup, and we argue that the ambiguities reported in the previous work can be understood as basis choices for gauge-invariant operators living in the buffer zone. The proposed procedure applies to Abelian theories with matter and with continuous symmetry groups, both on the lattice and in the continuum.