2012/07/20 by V. Zatloukal, Václav Zatloukal, Lauri Lehman +7 · 6 citations
Mathematics · Physics and Astronomy · #Abelian group #Anyon #Combinatorics #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Theoretical physics #Topological quantum computer #Topology (electrical circuits) #cond-mat.other #quant-ph
paper · pdf · doi:10.1103/physrevb.90.134201
published in Physical Review B 90(13) (American Physical Society) · 9 pages, 5 figures
arxiv created 2012/07/20 · openalex publication_date 2014/10/09 · arxiv updated 2014/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 behaviors are identified. We analytically demonstrate that all types of Abelian anyons localize purely due to the statistical phases induced by their random anyonic environment. In contrast, we numerically show that non-Abelian Ising anyons do not localize. This is due to their entanglement with the anyonic environment, which effectively induces dephasing. Our study demonstrates that localization properties strongly depend on nonlocal topological interactions, and it provides a clear distinction in the transport properties of Abelian and non-Abelian anyons.