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.

arXiv comment15 pages, 7 figures

References in corpus (43)

• Classification of topological insulators and superconductors in three spatial dimensions
• Photonic Floquet Topological Insulators
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Photovoltaic Hall effect in graphene
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Topological characterization of periodically-driven quantum systems
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Floquet Engineering of Quantum Materials
• Observation of topologically protected bound states in a one dimensional photonic system
• Exploring Topological Phases With Quantum Walks
• Topological Transition in a Non-Hermitian Quantum Walk
• Floquet-Bloch theory and topology in periodically driven lattices
• Floquet chiral edge states in graphene
• Topological singularities and the general classification of Floquet-Bloch systems
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Effective Hamiltonians for periodically driven systems
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Dynamical moments reveal a topological quantum transition in a photonic quantum walk
• Floquet symmetry-protected topological phases in cold atomic systems
• Topological phases and delocalization of quantum walks in random environments
• Floquet topological phases protected by time glide symmetry
• Floquet topological phases with symmetry in all dimensions
• Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk
• Measuring Topological Invariants in Disordered Discrete Time Quantum Walks
• Space-time crystal and space-time group
• Scattering theory of topological phases in discrete-time quantum walks
• The topological classification of one-dimensional symmetric quantum walks
• Bulk-edge correspondence of one-dimensional quantum walks
• Edge-state enhanced transport in a 2-dimensional quantum walk
• Floquet chiral magnetic effect
• Laser-induced topological superconductivity in cuprate thin films
• Higher winding number in a non-unitary photonic quantum walk
• Complete homotopy invariants for translation invariant symmetric quantum walks on a chain
• Supersymmetric polarization anomaly in photonic discrete-time quantum walks
• Attractor-repeller pair of topological zero-modes in a nonlinear quantum walk
• Eigenvalue Measurement of Topologically Protected Edge states in Split-Step Quantum Walks
• Laser control of magnonic topological phases in antiferromagnets
• Edge states in a two-dimensional quantum walk with disorder
• Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet systems
• Sensitivity of quantum walks to boundary of two-dimensional lattices: approaches from the CGMV method and topological phases

Cited by in corpus (8)

• Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
• 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
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step 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