A stabilization mechanism for many-body localization in two dimensions

D. C. W. Foo, N. Swain, P. Sengupta, G. Lemarié, S. Adam

Published 2022-02-18Version 1

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.