Emergent entanglement phase transitions in non-Hermitian Aubry-Andr\'e-Harper chains

TL;DR

This paper explores entanglement phase transitions in non-Hermitian Aubry-André-Harper chains, revealing a transition from skin-effect-induced to Anderson localization-induced area laws, with a volume law emerging at the critical point.

Contribution

It uncovers the existence of distinct entanglement phases and the phase transition between them in non-Hermitian quasiperiodic systems, highlighting the role of skin effect and Anderson localization.

Findings

Phase transition from skin effect to Anderson localization with increasing quasiperiodic strength

Non-monotonic entanglement entropy behavior in the skin-effect phase

Volume law emergence at the critical point between phases

Abstract

We investigate the entanglement dynamics of the non-Hermitian Aubry-Andr\'e-Harper (AAH) chain. The results reveal that by increasing quasiperiodic strength, a phase transition occurs from the area law induced by non-Hermitian skin effect to the area law arising from Anderson localization. For the former, the entanglement entropy follows a non-monotonic process, i.e., it increases first, then oscillates, and finally converges to a stable value. While for the latter, the entanglement entropy remains low because the wave function is not expandable in Anderson's localization region. The early-stage behavior of entanglement entropy indicates that the two area-law cases are of different phases. Interestingly, the volume-law behavior emerges at the critical point between these two area-law phases. Our study reveals that the area laws induced by the skin effect and the Anderson localization is two different phases, and that a volume law can emerge at the phase transition point. The understanding of the entanglement phase transition induced by disorder and skin effect is thus deepened.