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arXiv · 1609.09650

Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry

Ken Mochizuki·Dakyeong Kim·Norio Kawakami·Hideaki Obuse
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Abstract

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.

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Ken Mochizuki, Dakyeong Kim, Norio Kawakami, Hideaki Obuse. 2016-09-30. Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry. https://doi.org/10.1103/physreva.102.062202

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