On the stability of many-body localization in d>1

It was recently argued that MBL is unstable in two and higher dimensions due to a thermalization avalanche triggerred by rare regions of weak disorder [1]. We test these arguments using exact diagonalization (ED) studies as well as a solvable effective model. The ED results show excellent agreement with a refined theory of the thermalization avalanche that includes the transient finite size effects, lending strong support to the avalanche scenario. At the same time, the solvable model we analyze suggests a possible mode of failure of the avalanche. In this scheme we model the finite ergodic region using a Sachdev-Ye-Kitaev model and couple it to an Anderson insulator of non-interacting fermions. In a suitable large-N limit, we find that the spectral function of a local operator changes dramatically when coupled to a large number of Anderson fermions and can even undergo a dynamical phase transition. While this fact does not in itslef preclude the thermalization avalanche, it violates a central assumption in the arguments of Ref. [1].

[1] Wojciech De Roeck and Francois Huveneers, Phys. Rev. B 95, 155129 (2017).