A stabilization mechanism for many-body localization in two dimensions

TL;DR

This paper proposes that a confining potential can induce super-exponential localization in disordered systems, potentially stabilizing many-body localization in two dimensions and reconciling experimental observations with theoretical predictions.

Contribution

It demonstrates that Gaussian localization of LIOMs shifts the critical dimension for MBL stability from 1 to 2, challenging previous theoretical limitations.

Findings

Confining potentials lead to super-exponential (Gaussian) localization of wavefunctions.

Gaussian localization of LIOMs extends the MBL phase stability to two dimensions.

Experimental setups with confining potentials can realize stable MBL in 2D systems.

Abstract

Experiments in cold atom systems see almost identical signatures of many body localization (MBL) in both one-dimensional ($d=1$) and two-dimensional ($d=2$) systems despite the thermal avalanche hypothesis showing that the MBL phase is unstable for $d>1$. Underpinning the thermal avalanche argument is the assumption of exponential localization of local integrals of motion (LIOMs). In this work we demonstrate that addition of a confining potential -- as is typical in experimental setups -- allows a non-interacting disordered system to have super-exponentially (Gaussian) localized wavefunctions, and an interacting disordered system to undergo a localization transition. Moreover, we show that Gaussian localization of MBL LIOMs shifts the quantum avalanche critical dimension from $d=1$ to $d=2$, potentially bridging the divide between the experimental demonstrations of MBL in these systems and existing theoretical arguments that claim that such demonstrations are impossible.