Disorder-Induced Entanglement Phase Transitions in Non-Hermitian Systems with Skin Effects

Abstract:Non-Hermitian dynamics is ubiquitous in various physical systems. While recent study shows that such a dynamics leads to an area-law scaling of the entanglement entropy due to the non-Hermitian skin effects, it remains unclear how disorder changes the behavior of the entanglement entropy in a non-Hermitian system with skin effects. Here we study the dynamics of a many-body state of free fermions in the paradigmatic Hatano-Nelson model with open boundaries, and find that the area-law behavior of the entanglement entropy in the pristine Hatano-Nelson model develops into a logarithmic scaling for small disorder strength. As we further increase the disorder strength, the system reenters an area-law regime through an entanglement phase transition. At the critical point, the entanglement entropy exhibits a universal algebraic scaling. We further demonstrate the absence of a conformal invariance in the log-law regime by examining the subsystem entanglement entropy, the connected correlation function and the mutual information. Finally, we show the existence of disorder induced entanglement phase transitions in the Hatano-Nelson model with periodic boundaries.

Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Gases (cond-mat.quant-gas)

arXiv:2305.12342 [quant-ph]

(or arXiv:2305.12342v3 [quant-ph] for this version)