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Bulk-boundary correspondence for chiral symmetric quantum walks
| Title: | Bulk-boundary correspondence for chiral symmetric quantum walks |
| Authors: | Asboth, Janos K. Browse this author | | Obuse, Hideaki Browse this author |
| Issue Date: | 17-Sep-2013 |
| Publisher: | Amer physical soc |
| Journal Title: | Physical review b |
| Volume: | 88 |
| Issue: | 12 |
| Start Page: | 121406 |
| Publisher DOI: | 10.1103/PhysRevB.88.121406 |
| Abstract: | 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. |
| Rights: | ©2013 American Physical Society |
| Type: | article |
| URI: | http://hdl.handle.net/2115/53443 |
| Appears in Collections: | 工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 小布施 秀明
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