Transport properties of anyons in random topological environments

TL;DR

This paper investigates how Abelian and non-Abelian anyons behave in random topological environments, revealing that Abelian anyons localize while non-Abelian ones do not, due to their different quantum interactions.

Contribution

It provides the first analytical proof of Abelian anyon localization and numerical evidence of non-Abelian anyon delocalization in disordered topological systems.

Findings

Abelian anyons localize due to statistical phases.

Non-Abelian Ising anyons do not localize.

Transport properties depend on topological interactions.

Abstract

The quasi one-dimensional transport of Abelian and non-Abelian anyons is studied in the presence of a random topological background. In particular, we consider the quantum walk of an anyon that braids around islands of randomly filled static anyons of the same type. Two distinct behaviours are identified. We analytically demonstrate that all types of Abelian anyons localise purely due to the statistical phases induced by their random anyonic environment. In contrast, we numerically show that non-Abelian Ising anyons do not localise. This is due to their entanglement with the anyonic environment that effectively induces dephasing. Our study demonstrates that localisation properties strongly depend on non-local topological interactions and it provides a clear distinction in the transport properties of Abelian and non-Abelian statistics.