Entanglement Entropy of Topological Orders with Boundaries

TL;DR

This paper investigates how boundary conditions affect entanglement entropy in 2+1D topological orders, especially non-Abelian ones, introducing an efficient computation method that reproduces known results with anyonic excitations.

Contribution

It presents a streamlined, efficient method to compute entanglement entropy in topological orders with boundaries, highlighting boundary condition effects, especially in non-Abelian cases.

Findings

Entanglement entropy depends strongly on boundary conditions.

The new method efficiently reproduces known results for systems with anyonic excitations.

Non-Abelian topological orders show particularly interesting boundary-dependent entropy behavior.

Abstract

In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum double. We will find very interesting dependence of the entanglement entropy on the boundary conditions particularly when the system is non-Abelian. Along the way, we demonstrate a streamlined procedure to compute the entanglement entropy, which is particularly efficient when dealing with systems with boundaries. We also show how this method efficiently reproduces all the known results in the presence of anyonic excitations.