Topological boundary invariants for Floquet systems and quantum walks

Abstract

A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only depend on the bands of the Floquet operator or also on the time as a variable. It is shown how a K-theoretic result combined with the bulk-boundary correspondence leads to edge invariants for the half-space Floquet operators. These results also apply to topological quantum walks.

arXiv commentCorrection of several misprints, added references, to appear in Mathematical Physics, Analysis, Geometry

References in corpus (12)

• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological singularities and the general classification of Floquet-Bloch systems
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Network Models of Photonic Floquet Topological Insulators
• Simultaneous quantization of edge and bulk Hall conductivity
• Complex classes of periodically driven topological lattice systems
• Equality of bulk and edge Hall conductance revisited
• Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian
• Phase rotation symmetry and the topology of oriented scattering networks
• Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals
• Spectral Stability of Unitary Network Models

Cited by in corpus (15)

• Topology and Broken Symmetry in Floquet Systems
• Bulk-Edge correspondence for two-dimensional Floquet topological insulators
• On the Bott index of unitary matrices on a finite torus
• Complete homotopy invariants for translation invariant symmetric quantum walks on a chain
• Strongly Disordered Floquet Topological Systems
• Time-dependent topological systems: A study of the Bott index
• Singular continuous Cantor spectrum for magnetic quantum walks
• Topological chiral modes in random scattering networks
• Chiral Flow in One-dimensional Floquet Topological Insulators
• Effective vacua for Floquet topological phases: A numerical perspective on switch-function formalism
• Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Bulk-Boundary Correspondence for Topological Insulators with Quantized Magneto-Electric Effect
• Eigenvalue crossings in Floquet topological systems