Topological Quantum Walk with Discrete Time-Glide Symmetry

• URL: http://arxiv.org/abs/2004.09332v3
• Date: Wed, 15 Jul 2020 10:35:37 GMT
• Title: Topological Quantum Walk with Discrete Time-Glide Symmetry
• Authors: Ken Mochizuki, Takumi Bessho, Masatoshi Sato, and Hideaki Obuse
• Abstract summary: We formulate discrete space-time symmetry in quantum walks and evaluate the corresponding symmetry protected topological phases. Due to discrete nature of time evolution, the topological classification is found to be different from that in conventional Floquet systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary operators. Regarding each constituent unitary operator as a discrete time step, we formulate discrete space-time symmetry in quantum walks and evaluate the corresponding symmetry protected topological phases. In particular, we study chiral and/or time-glide symmetric topological quantum walks in this formalism. Due to discrete nature of time evolution,the topological classification is found to be different from that in conventional Floquet systems. As a concrete example, we study a two-dimensional quantum walk having both chiral and time-glide symmetries, and identify the anomalous edge states protected by these symmetries.

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