Localization of a mobile impurity interacting with an Anderson insulator

TL;DR

This paper investigates whether a mobile impurity can destabilize localization in an Anderson insulator, combining analytical criteria with numerical simulations, and finds evidence supporting the stability of localization despite the impurity.

Contribution

It introduces an analytic criterion for localization stability and compares dynamical Hartree and TEBD simulations, demonstrating the impurity's localization persistence.

Findings

Dynamical Hartree predicts delocalization, while TEBD suggests stability.

Impurity remains localized in eigenstates, with localized entanglement.

Numerical evidence supports the robustness of Anderson localization against a mobile impurity.

Abstract

Thermalizing and localized many-body quantum systems present two distinct dynamical phases of matter. Recently, the fate of a localized system coupled to a thermalizing system viewed as a quantum bath received significant theoretical and experimental attention. In this work, we study a mobile impurity, representing a small quantum bath, that interacts locally with an Anderson insulator with a finite density of localized particles. Using static Hartree approximation to obtain an effective disorder strength, we formulate an analytic criterion for the perturbative stability of the localization. Next, we use an approximate dynamical Hartree method and the quasi-exact time-evolved block decimation (TEBD) algorithm to study the dynamics of the system. We find that the dynamical Hartree approach which completely ignores entanglement between the impurity and localized particles predicts the delocalization of the system. In contrast, the full numerical simulation of the unitary dynamics with TEBD suggests the stability of localization on numerically accessible timescales. Finally, using an extension of the density matrix renormalization group algorithm to excited states (DMRG-X), we approximate the highly excited eigenstates of the system. We find that the impurity remains localized in the eigenstates and entanglement is enhanced in a finite region around the position of the impurity, confirming the dynamical predictions. Dynamics and the DMRG-X results provide compelling evidence for the stability of localization.