| Abstract: | We consider the question whether there could be many-body localization in an interacting disordered system in two or higher dimension. We discuss some recent arguments suggesting that, for any dimension higher than one, a localized system is unstable even in the presence of a single finite thermal region within the insulator. We discuss some preliminary numerical tests of the arguments via exact diagonalization for small systems. To consider the thermodynamic limit, we construct a solvable large-N model of Anderson localized sites coupled to a thermal region described via a Sachdev-Ye-Kitaev model, that exhibits quantum chaos and themalization. We show that the coupled system exhibits a dynamical phase transition from a chaotic quantum liquid to a non-chaotic quadratic fixed point as a function of the coupling strength or the localization length of the insulator. Based on this we argue that, contrary to the proposition, the thermal region actually might get proximity localized due to the surrounding insulator, rendering MBL stable in higher dimension. |