Aspects of Entanglement Entropy for Gauge Theories

TL;DR

This paper investigates the properties of entanglement entropy in Non-Abelian gauge theories using an extended Hilbert space approach, revealing differences from Abelian cases and connecting to topological quantum dimensions.

Contribution

It extends the electric centre definition to Non-Abelian gauge theories, compares entanglement entropy with Bell pair extraction, and computes topological entanglement entropy in non-Abelian models.

Findings

Extended the electric centre definition for Non-Abelian theories.

Found entanglement entropy differs from Bell pair bounds.

Computed topological entanglement entropy matching quantum dimensions.

Abstract

A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories. We extend the electric centre definition of Casini, Huerta and Rosabal to the Non-Abelian case and find that it differs in an important term. We also find that the entanglement entropy does not agree with the maximum number of Bell pairs that can be extracted by the processes of entanglement distillation or dilution, and give protocols which achieve the maximum bound. Finally, we compute the topological entanglement entropy which follows from the extended Hilbert space definition and show that it correctly reproduces the total quantum dimension in a class of Toric code models based on Non-Abelian discrete groups.