open access

https://hdl.handle.net/2115/53443

Bulk-boundary correspondence for chiral symmetric quantum walks

英語

2013-09-17

Amer physical soc

Physical review b

88(12)

121406

Discrete-time quantum walks (DTQW) have topological phases that are richer than those of time-independent lattice Hamiltonians. Even the basic symmetries, on which the standard classification of topological insulators hinges, have not yet been properly defined for quantum walks. We introduce the key tool of time frames, i.e., we describe a DTQW by the ensemble of time-shifted unitary time-step operators belonging to the walk. This gives us a way to consistently define chiral symmetry (CS) for DTQW's. We show that CS can be ensured by using an "inversion symmetric" pulse sequence. For one-dimensional DTQW's with CS, we identify the bulk Z x Z topological invariant that controls the number of topologically protected 0 and pi energy edge states at the interfaces between different domains, and give simple formulas for these invariants. We illustrate this bulk-boundary correspondence for DTQW's on the example of the "4-step quantum walk," where tuning CS and particle-hole symmetry realizes edge states in various symmetry classes.

学術雑誌論文

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©2013 American Physical Society

1098-0121