Two-dimensional quantum walk with non-Hermitian skin effects

TL;DR

This paper demonstrates a two-dimensional non-Hermitian quantum walk exhibiting skin effects, confirming the bulk-boundary correspondence through non-Bloch topological invariants and advancing understanding of non-Hermitian Floquet topological phases.

Contribution

It introduces a novel 2D non-Hermitian quantum walk model with skin effects and develops a non-Bloch band theory to analyze its topological properties.

Findings

Topological edge states are consistent with Floquet winding numbers.

Non-Bloch topological invariants are captured by a non-Hermitian local Chern marker.

Skin effects are integral to the topological characterization of the system.

Abstract

We construct a two-dimensional, discrete-time quantum walk exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states are consistent with Floquet winding numbers calculated using a non-Bloch band theory invoking time-dependent generalized Billouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined through local biorthogonal eigen wave functions of the non-unitary Floquet operator. Our work would stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.