Helical damping and dynamical critical skin effect in open quantum systems

Chun-Hui Liu,Kai Zhang,Zhesen Yang,Shu Chen

doi:10.1103/physrevresearch.2.043167

Abstract

Non-Hermitian skin effect and critical skin effect are unique features of non-Hermitian systems. In this Letter, we study an open system with its dynamics of single-particle correlation function effectively dominated by a non-Hermitian damping matrix, which exhibits $\mathbb{Z}_2$ skin effect, and uncover the existence of a novel phenomenon of helical damping. When adding perturbations that break anomalous time reversal symmetry to the system, the critical skin effect occurs, which causes the disappearance of the helical damping in the thermodynamic limit although it can exist in small size systems. We also demonstrate the existence of anomalous critical skin effect when we couple two identical systems with $\mathbb{Z}_2$ skin effect. With the help of non-Bloch band theory, we unveil that the change of generalized Brillouin zone equation is the necessary condition of critical skin effect.

Highlights

When the time-reversal symmetry is broken by adding perturbations, we find the occurrence of dynamical critical skin effect, which causes the disappearance of the helical damping in the thermodynamic limit it can survive in small size systems
We find that the coupled subsystems with same generalized Brillouin zone (GBZ) can exhibit CSE, for which we call it anomalous critical skin effect, and give an example that coupled subsystems with different GBZs do not support CSE
We have unveiled the occurrence of helical damping in the open quantum system with Z2 skin effect if the open boundary spectrum of the damping matrix is gapped and the periodic boundary spectrum is gapless

Summary

INTRODUCTION

Non-Hermitian systems are attracting growing attention as they demonstrate some novel properties without Hermitian counterparts [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] and many physical problems in photonic systems, electrical systems and open quantum systems can be converted to non-Hermitian Hamiltonian problems [22,23,24,25,26,27,28]. One of unique features of non-Hermitian systems is the non-Hermitian skin effect [13], which is characterized by the emergence of the majority of eigenstates accumulated at one of the boundaries with a remarkably different eigenvalue spectral under the open versus periodic boundary conditions, and breakdown of conventional bulk boundary correspondence [12,13,14,49,50,51,52,53,54,55,56,57,58,59,60,61] Both phenomena can be understood in the scheme of non-Bloch band theory by introducing the concept of the generalized Brillouin zone (GBZ), which is composed. We find that the coupled subsystems with same GBZs can exhibit CSE, for which we call it anomalous critical skin effect, and give an example that coupled subsystems with different GBZs do not support CSE We shall explain these phenomena and demonstrate that the change of the GBZ equation is the necessary condition of CSE, as long as the non-Bloch band theory works.

HELICAL DAMPING

DYNAMICAL CRITICAL SKIN EFFECT

SUMMARY AND DISCUSSION