Transport properties of anyons in random topological environments

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.

arXiv comment9 pages, 5 figures

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Cited by in corpus (6)

• Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics
• Thermalization of Topological Entropy after a Quantum Quench
• Simulation of braiding anyons using Matrix Product States
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Numerical simulation of non-abelian anyons
• Studies of braided non-Abelian anyons using anyonic tensor networks