Chiral Floquet Systems and Quantum Walks at Half-Period

verfasst von

C. Cedzich, T. Geib, A. H. Werner, R. F. Werner

Abstract

We classify chiral symmetric periodically driven quantum systems on a one-dimensional lattice. The driving process is local, can be continuous, or discrete in time, and we assume a gap condition for the corresponding Floquet operator. The analysis is in terms of the unitary operator at a half-period, the half-step operator. We give a complete classification of the connected classes of half-step operators in terms of five integer indices. On the basis of these indices, it can be decided whether the half-step operator can be obtained from a continuous Hamiltonian driving, or not. The half-step operator determines two Floquet operators, obtained by starting the driving at zero or at half-period, respectively. These are called timeframes and are chiral symmetric quantum walks. Conversely, we show under which conditions two chiral symmetric walks determine a common half-step operator. Moreover, we clarify the connection between the classification of half-step operators and the corresponding quantum walks. Within this theory, we prove bulk-edge correspondence and show that a second timeframe allows to distinguish between symmetry protected edge states at +1 and -1 which is not possible for a single timeframe.

Organisationseinheit(en)

Institut für Theoretische Physik
SFB 1227: Designte Quantenzustände der Materie (DQ-mat)

Externe Organisation(en)

Universite Paris-Sud
University of Copenhagen

Typ

Artikel

Journal

Annales Henri Poincare

Band

22

Seiten

375-413

Anzahl der Seiten

39

ISSN

1424-0637

Publikationsdatum

02.2021

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Statistische und nichtlineare Physik, Kern- und Hochenergiephysik, Mathematische Physik

Elektronische Version(en)

https://arxiv.org/abs/2006.04634 (Zugang: Offen)
https://doi.org/10.1007/s00023-020-00982-6 (Zugang: Geschlossen)