Unusual wave-packet spreading and entanglement dynamics in non-Hermitian disordered many-body systems

TL;DR

This paper explores how non-Hermiticity and disorder influence wave-packet spreading and entanglement dynamics in quantum systems, revealing unconventional behaviors near localization transitions and a non-monotonic entanglement evolution.

Contribution

It demonstrates the distinct wave packet and entanglement behaviors in non-Hermitian disordered systems, highlighting the role of dephasing and disorder in these dynamics.

Findings

Wave packet spreading is suppressed in the clean limit and weak disorder but revives near the localization transition.

Entanglement entropy exhibits non-monotonic time evolution in non-Hermitian systems.

A crossover from area-law to volume-law entanglement entropy is observed with increasing disorder.

Abstract

Non-Hermiticity and dephasing, collaborating in an unusual wave packet dynamics, realizes unconventional entanglement evolution in a disordered, interacting and asymmetric (non-reciprocal) quantum medium. Taking the Hatano-Nelson model as a concrete example, we first consider how wave packet spreads in a non-Hermitian disordered system for demonstraing that it is very different from the Hermitian case. Interestingly, a cascade like wave packet spreading as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity of the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in the interacting non-Hermitian model, revealing its non-monotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy in Hermitian and non-Hermitian systems, and show that the many-body dynamics is governed by a principle different from the Hermitian case. The size dependence of the results suggests with the increase of disorder, a unusual area-volume-area law crossover of the maximal entanglement entropy. To analyze the effects of disorder on a firm basis, using the Hermitian limit as a benchmark, we employ a quasi-periodic disorder (Aubry-Andr\'{e} model) in the analyses.