TY - JOUR

T1 - Chiral Floquet Systems and Quantum Walks at Half-Period

AU - Cedzich, C.

AU - Geib, T.

AU - Werner, A. H.

AU - Werner, R. F.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85098510508&partnerID=8YFLogxK

U2 - 10.1007/s00023-020-00982-6

DO - 10.1007/s00023-020-00982-6

M3 - Journal article

AN - SCOPUS:85098510508

VL - 22

SP - 375

EP - 413

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 2

ER -