Localization, delocalization, and topological transitions in disordered two-dimensional quantum walks
2015 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 91, no 10, 104202Article in journal (Refereed) Published
We investigate time-independent disorder on several two-dimensional discrete-time quantum walks. We find numerically that, contrary to claims in the literature, random onsite phase disorder, spin-dependent or otherwise, cannot localize the Hadamard quantum walk; rather, it induces diffusive spreading of the walker. In contrast, split-step quantum walks are generically localized by phase disorder. We explain this difference by showing that the Hadamard walk is a special case of the split-step quantum walk, with parameters tuned to a critical point at a topological phase transition. We show that the topological phase transition can also be reached by introducing strong disorder in the rotation angles. We determine the critical exponent for the divergence of the localization length at the topological phase transition, and find nu = 2.6, in both cases. This places the two-dimensional split-step quantum walk in the universality class of the quantum Hall effect.
Place, publisher, year, edition, pages
2015. Vol. 91, no 10, 104202
IdentifiersURN: urn:nbn:se:su:diva-116627DOI: 10.1103/PhysRevB.91.104202ISI: 000350845400003OAI: oai:DiVA.org:su-116627DiVA: diva2:808084