Response to a local quench of a system near many body localization transition

TL;DR

This paper investigates how a disordered spin chain near the many-body localization transition responds to local perturbations, proposing a method to determine the mobility edge and characterize localization length through local measurements.

Contribution

It introduces a novel approach for accurately identifying the mobility edge and localization length in MBL systems using local spin response analysis.

Findings

Exponential decay of spin response with distance characterizes localization length.

Method enables precise determination of the mobility edge in disordered spin chains.

Local measurements can effectively distinguish between localized and delocalized phases.

Abstract

We consider a one dimensional spin $1/2$ chain with Heisenberg interaction in a disordered parallel magnetic field. This system is known to exhibit the many body localization (MBL) transition at critical strength of disorder. We analyze the response of the chain when additional perpendicular magnetic field is applied to an individual spin and propose a method for accurate determination of the mobility edge via local spin measurements. We further demonstrate that the exponential decrease of the spin response with the distance between perturbed spin and measured spin can be used to characterize the localization length in the MBL phase.