Absence of many-body localization in a continuum

Understand

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.