Chiral Floquet Systems and Quantum Walks at Half-Period

authored by

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.

Organisation(s)

Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)

External Organisation(s)

Universite Paris-Sud
University of Copenhagen

Type

Article

Journal

Annales Henri Poincare

Volume

22

Pages

375-413

No. of pages

39

ISSN

1424-0637

Publication date

02.2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics, Nuclear and High Energy Physics, Mathematical Physics

Electronic version(s)

https://arxiv.org/abs/2006.04634 (Access: Open)
https://doi.org/10.1007/s00023-020-00982-6 (Access: Closed)