Stabilization mechanism for many-body localization in two dimensions

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 (LIOM). In this Letter we demonstrate that the addition of a confining potential-as is typical in experimental setups-allows a noninteracting disordered system to have superexponentially (Gaussian) localized wave functions, and an interacting disordered system to undergo a localization transition. Moreover, we show that Gaussian localization of MBL LIOM 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.