Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2016
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| _version_ | 1866929666103705600 |
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| author | Mochizuki, Ken Kim, Dakyeong Kawakami, Norio Obuse, Hideaki |
| author_facet | Mochizuki, Ken Kim, Dakyeong Kawakami, Norio Obuse, Hideaki |
| contents | We study topological phases in one-dimensional open Floquet systems driven by chiral symmetric nonunitary time evolution. We derive a procedure to calculate topological numbers from nonunitary time-evolution operators with chiral symmetry. While the procedure has been applied to open Floquet systems described by nonunitary time-evolution operators, we give the microscopic foundation and clarify its validity for the first time. We construct a model of chiral symmetric nonunitary quantum walks classified into class BDI$^\dagger$ or AIII, which is one of enlarged symmetry classes for topological phases in open systems, based on experiments of discrete-time quantum walks. Then, we confirm that the topological numbers obtained from the derived procedure give correct predictions of the emergent edge states. We also show that the model retains $\mathcal{PT}$ symmetry in certain cases and its dynamics is crucially affected by the presence or absence of $\mathcal{PT}$ symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1609_09650 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry Mochizuki, Ken Kim, Dakyeong Kawakami, Norio Obuse, Hideaki Mesoscale and Nanoscale Physics Optics Quantum Physics We study topological phases in one-dimensional open Floquet systems driven by chiral symmetric nonunitary time evolution. We derive a procedure to calculate topological numbers from nonunitary time-evolution operators with chiral symmetry. While the procedure has been applied to open Floquet systems described by nonunitary time-evolution operators, we give the microscopic foundation and clarify its validity for the first time. We construct a model of chiral symmetric nonunitary quantum walks classified into class BDI$^\dagger$ or AIII, which is one of enlarged symmetry classes for topological phases in open systems, based on experiments of discrete-time quantum walks. Then, we confirm that the topological numbers obtained from the derived procedure give correct predictions of the emergent edge states. We also show that the model retains $\mathcal{PT}$ symmetry in certain cases and its dynamics is crucially affected by the presence or absence of $\mathcal{PT}$ symmetry. |
| title | Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry |
| topic | Mesoscale and Nanoscale Physics Optics Quantum Physics |
| url | https://arxiv.org/abs/1609.09650 |