Stabilization mechanism for many-body localization in two dimensions

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