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.

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

References in corpus (2)

• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals

Cited by in corpus (2)

• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model