Topological Quantum Walk with Discrete Time-Glide Symmetry

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.

15 pages, 7 figures

References in corpus (10)

• Classification of topological insulators and superconductors in three spatial dimensions
• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
• Exploring Topological Phases With Quantum Walks
• Topological Transition in a Non-Hermitian Quantum Walk
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
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• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Edge-state enhanced transport in a 2-dimensional quantum walk
• Laser control of magnonic topological phases in antiferromagnets

Cited by in corpus (7)

• Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems
• Massless Dirac fermions on a space-time lattice with a topologically protected Dirac cone
• Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Relative homotopy approach to topological phases in quantum walks
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• The mixing-spacetime symmetry in the Floquet-Bloch band theory