Splitting the Topological Degeneracy of non-Abelian Anyons

TL;DR

This paper analyzes how tunneling interactions between non-Abelian anyons lift their topological degeneracy, showing that such effects are generally destructive to topological protection at short distances.

Contribution

It provides a detailed theoretical framework connecting tunneling processes to the algebraic structure of non-Abelian anyons and quantifies degeneracy lifting effects.

Findings

Tunneling lifts topological degeneracy of non-Abelian anyons.

Degeneracy splitting is exponentially suppressed at large distances.

Interactions can be modeled as effective tunneling of topological charge.

Abstract

We examine tunneling of topological charge between non-Abelian anyons as a perturbation of the long-range effective theory of a topologically ordered system. We obtain energy corrections in terms of the anyons' universal algebraic structure and non-universal tunneling amplitudes. We find that generic tunneling completely lifts the topological degeneracy of non-Abelian anyons. This degeneracy splitting is exponentially suppressed for long distances between anyons, but leaves no topological protection at shorter distances. We also show that general interactions of anyons can be expressed in terms of the transfer of topological charge, and thus can be treated effectively as tunneling interactions.