Entanglement Phase Transition in Chaotic non-Hermitian Systems

TL;DR

This paper investigates an entanglement phase transition in chaotic non-Hermitian spin chains, revealing a dissipation-induced transition with unusual spectral and entanglement behaviors.

Contribution

It uncovers an exotic entanglement transition in chaotic non-Hermitian many-body systems, highlighting non-monotonic spectral gaps and unexpected entanglement features.

Findings

Spectral gap oscillations before gapped phase transition

Steady-state entanglement shifts from volume-law to area-law with dissipation

Level crossings explain unusual spectral and entanglement behaviors

Abstract

We study an entanglement phase transition in a class of chaotic non-Hermitian spin chains whose spin-spin coupling terms commute with the non-Hermitian contributions. Two representative models are investigated: the transverse-field Ising model with a complex longitudinal field and the non-Hermitian XX model with a transverse field. By analyzing their complex spectra, we find that both models undergo a dissipation-induced gapless-gapped phase transition when the transverse field exceeds a model-dependent threshold. Interestingly, the complex gap does not vary monotonically with the dissipation rate; instead, it exhibits pronounced oscillations before entering the gapped phase. By simulating their non-unitary dynamics, we show that the steady-state entanglement entropy undergoes a transition from volume-law to area-law scaling as the dissipation rate increases. Moreover, several unexpected features emerge within the volume-law regime: a larger complex gap or dissipation rate may lead to a more entangled steady state. We trace these unusual behaviors of the complex gap and the steady-state entanglement to level crossings between the maximal imaginary level and other spectral levels. Our work uncovers an exotic entanglement transition in chaotic non-Hermitian many-body systems.