A stabilisation mechanism for many body localisation in 2D

Experiments in cold atom systems see identical signatures of many body localisation (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 localisation of local integrals of motion (LIOMs), a result taken from the Furstenberg theorem. In this work we show that the Furstenberg theorem assumptions break down for real experimental systems, resulting in super-exponential localisation of LIOMs. A more careful analysis of the quantum avalanche argument for such realistic systems shows that the critical dimension changes from d=1 to d=2, thereby bridging the divide between the experimental demonstrations of MBL in these systems and existing theoretical arguments that claim that such demonstrations are impossible.