Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit

At the many-body localization transition, the dynamics of an isolated quantum system freezes out. In systems with long-range interactions (and possibly short-range systems in many spatial dimensions) this transition does not happen in the conventional thermodynamic limit: arbitrarily weak interactions prevent many-body localization. Here, the authors argue that even in these cases a sharp phase transition exists if one scales down the interaction strength with increasing system size in a specific nonstandard way.