Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry

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${}^{†}$ 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 $\mathcal{P}\mathcal{T}$ symmetry in certain cases and its dynamics is crucially affected by the presence or absence of $\mathcal{P}\mathcal{T}$ symmetry.

12 pages, 6 figures

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• PT Symmetric Floquet Topological Phase in SSH Model
• Symmetry and topological classification of Floquet non-Hermitian systems
• Connecting active and passive $\mathcal{P}\mathcal{T}$-symmetric Floquet modulation models
• Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension
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