Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry

TL;DR

This paper develops a method to calculate topological invariants in one-dimensional nonunitary Floquet systems with chiral symmetry, and validates it through a quantum walk model exhibiting edge states and symmetry effects.

Contribution

It provides the first microscopic foundation for calculating topological numbers in nonunitary Floquet systems with chiral symmetry, confirming their predictive power for edge states.

Findings

Derived a procedure for topological numbers in nonunitary systems

Constructed a chiral symmetric quantum walk model

Confirmed topological predictions match edge state emergence

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.