Slow dynamics of a mobile impurity interacting with an Anderson insulator

TL;DR

This paper studies the slow and transient dynamics of a mobile impurity in an Anderson insulator, revealing eventual sub-diffusive spreading and delocalization, with implications for understanding many-body localization phenomena.

Contribution

It demonstrates that slow dynamics and apparent many-body localization are transient, leading to eventual delocalization and sub-diffusive behavior in the system.

Findings

Impurity spreads sub-diffusively at long times

Density correlations decay as a power law

Entanglement entropy grows as a power law

Abstract

We investigate dynamics of a single mobile impurity immersed in a bath of Anderson localized particles and focus on the regime of relatively strong disorder and interactions. In that regime, the dynamics of the system is particularly slow, suggesting, at short times, an occurrence of many-body localization. Considering longer time scales, we show that the latter is a transient effect and that, eventually, the impurity spreads sub-diffusively and induces a gradual delocalization of the Anderson insulator. The phenomenology of the system in the considered regime of slow dynamics includes a sub-diffusive growth of mean square displacement of the impurity, power-law decay of density correlation functions of the Anderson insulator and a power-law growth of entanglement entropy in the system. We observe a similar regime of slow dynamics also when the disorder in the system is replaced by a sufficiently strong quasi-periodic potential.