Topological boundary invariants for Floquet systems and quantum walks

TL;DR

This paper develops topological invariants for Floquet systems and quantum walks, linking spectral gaps to bulk and edge properties through K-theory and bulk-boundary correspondence.

Contribution

It introduces a K-theoretic framework for defining boundary invariants in Floquet systems and quantum walks, extending topological classification methods.

Findings

Topological invariants depend on spectral gaps and possibly on time.

Edge invariants are derived for half-space Floquet operators.

Results unify bulk-boundary correspondence in driven quantum systems.

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.