Non-Bloch quench dynamics

Tianyu Li,Jia-Zheng Sun,Yong-Sheng Zhang,Wei Yi

doi:10.1103/physrevresearch.3.023022

Tianyu Li, Jia-Zheng Sun + Show 2 more

Open Access

https://doi.org/10.1103/physrevresearch.3.023022

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Abstract

We study the quench dynamics of non-Hermitian topological models with non-Hermitian skin effects. Adopting the non-Bloch band theory and projecting quench dynamics onto the generalized Brillouin zone, we find that emergent topological structures, in the form of dynamic skyrmions, exist in the generalized momentum-time domain, and are correlated with the non-Bloch topological invariants of the static Hamiltonians. The skyrmion structures anchor on the fixed points of dynamics whose existence are conditional on the coincidence of generalized Brillouin zones of the pre- and post-quench Hamiltonians. Global signatures of dynamic skyrmions, however, persist well beyond such a condition, thus offering a general dynamic detection scheme for non-Bloch topology in the presence of non-Hermitian skin effects. Applying our theory to an experimentally relevant, non-unitary quantum walk, we explicitly demonstrate how the non-Bloch topological invariants can be revealed through the non-Bloch quench dynamics.

Highlights

Non-Hermitian Hamiltonians arise in open systems [1,2], and have attracted significant attention [3,4,5,6,7,8,9,10]
Adopting the non-Bloch band theory and projecting quench dynamics onto the generalized Brillouin zone, we find that emergent topological structures, in the form of dynamic skyrmions, exist in the generalized momentumtime domain, and are correlated with the non-Bloch topological invariants of the static Hamiltonians
Applying our theory to an experimentally relevant, nonunitary quantum walk, we explicitly demonstrate how the non-Bloch topological invariants can be revealed through the non-Bloch quench dynamics

Summary

INTRODUCTION

Non-Hermitian Hamiltonians arise in open systems [1,2], and have attracted significant attention [3,4,5,6,7,8,9,10]. For a system possessing non-Hermitian skin effects, the associated Bloch spectra in the BZ necessarily form loops in the complex plane [21,22], such that real eigenspectra only exist in the GBZ under OBCs, protected by a non-Bloch PT symmetry [32,56,57]. We circumvent these issues by projecting the quench dynamics onto the generalized momentum sectors of the GBZ. We illustrate the extraction of non-Bloch winding numbers from the non-Bloch quench dynamics, using the recently implemented, nonunitary topological quantum walk

QUENCHING IN THE GBZ

BEYOND THE SIMPLE CASE

NONUNITARY QUANTUM WALK

CONCLUSION