Topological phases and delocalization of quantum walks in random environments

Hideaki Obuse and Norio Kawakami
Phys. Rev. B 84, 195139 – Published 28 November 2011

Abstract

We investigate one-dimensional (1D) discrete-time quantum walks (QWs) with spatially or temporally random defects as a consequence of interactions with random environments. We focus on the QWs with chiral symmetry in a topological phase, and reveal that chiral symmetry together with the bipartite nature of the QWs brings about intriguing behaviors such as coexistence of topologically protected edge states at zero energy and Anderson transitions in the 1D chiral class at nonzero energy in their dynamics. In contrast to results of previous studies, therefore, the spatially disordered QWs can avoid complete localization due to the Anderson transition. It is further confirmed that the edge states are robust to spatial disorder but not to temporal disorder.

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  • Received 28 August 2011

DOI:https://doi.org/10.1103/PhysRevB.84.195139

©2011 American Physical Society

Authors & Affiliations

Hideaki Obuse* and Norio Kawakami

  • Department of Physics, Kyoto University, Kyoto 606-8502, Japan

  • *Present address: Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany.

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Issue

Vol. 84, Iss. 19 — 15 November 2011

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