Absence of many-body mobility edges

Phenomenon of many-body localization violates one of the basic rules of statistical mechanics: It states that certain `localized' macroscopic systems cannot act as a bath for themselves and hence do not relax to equilibrium. The authors of this paper find that, whenever a system is not localized at all thermodynamic parameters (particle density, energy density), then local fluctuations into the non-localized phase, dubbed bubbles, can slowly destroy localization globally. This result provides a rather strong restriction on the existence of many-body localized phases and runs contrary to the idea that there could be genuine localization transitions as a function of temperature.