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We consider an extended electronic system with localized single‐particle states coupled by short‐range interactions, in the absence of coupling to an external bath. We show that many‐body localization, which exists in tight‐binding models, is unstable in a continuum. Irrespective of the dimensionality of the system, many‐body localization does not survive the unbounded growth of the single‐particle localization length with increasing energy that is characteristic of the continuum limit. The system remains delocalized down to arbitrarily small temperature  T , although its dynamics slows down as  T  decreases. Remarkably, the conductivity vanishes with decreasing  T  faster than in the Arrhenius law. The system can be characterized by an effective  T ‐dependent single‐particle mobility edge which diverges in the limit of    T  →  0   . Delocalization is driven by interactions between hot electrons above the mobility edge and the “bath” of thermal electrons in the vicinity of the Fermi level.

Absence of many‐body localization in a continuum