Many body localization and delocalization in the two dimensional continuum

Understand

I discuss whether localization in the two dimensional continuum can be stable in the presence of short range interactions.

• I conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature $T < T_c$, then perturbation theory about the localized phase converges almost everywhere.
• As a result, the system is at least asymptotically localized, and perhaps even truly many body localized, depending on how certain rare regions behave.
• Meanwhile, for $T > T_c$, perturbation theory fails to converge, which I interpret as interaction mediated delocalization.