Two-dimensional quantum walk with non-Hermitian skin effects

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.

arXiv comment8 pages, 4 figures

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• Topological Non-Hermitian skin effect
• Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals
• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Entanglement Entropy of Non-Hermitian Free Fermions
• Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
• Non-Bloch quench dynamics
• Inner non-Hermitian skin effect on Bethe lattice
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Investigating the quench dynamics of the bound states in a spin-orbital coupling system using a trapped ion
• Emergent Weyl-like points in periodically modulated systems