Chiral Floquet Systems and Quantum Walks at Half-Period
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- Chiral Floquet systems and quantum walks at half period-Preprint
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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.
Original language | English |
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Journal | Annales Henri Poincare |
Volume | 22 |
Issue number | 2 |
Pages (from-to) | 375-413 |
ISSN | 1424-0637 |
DOIs | |
Publication status | Published - 2021 |
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