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

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