Topological Entanglement Entropy with a Twist

TL;DR

This paper uses topological entanglement entropy to analyze defects called twists in the toric code, revealing their equivalence to Ising anyons in terms of quantum dimensions and fusion rules.

Contribution

It demonstrates that twists and dyons in the toric code share key properties with Ising anyons using entanglement entropy as a diagnostic tool.

Findings

Twists and dyons in the toric code have the same quantum dimensions as Ising anyons.

The total quantum dimension of the model matches that of the Ising anyon model.

Fusion rules for twists and dyons align with those of Ising anyons.

Abstract

Defects in topologically ordered models have interesting properties that are reminiscent of the anyonic excitations of the models themselves. For example, dislocations in the toric code model are known as twists and possess properties that are analogous to Ising anyons. We strengthen this analogy by using the topological entanglement entropy as a diagnostic tool to identify properties of both defects and excitations in the toric code. Specifically, we show, through explicit calculation, that the toric code model including twists and dyon excitations has the same quantum dimensions, the same total quantum dimension, and the same fusion rules as an Ising anyon model.