Instability of localization in translation-invariant systems

Understand

The phenomenon of localization is usually accompanied with the presence of quenched disorder.

• To what extent disorder is necessary for localization is a well-known open problem.
• In this paper, we prove the instability of localization in translation-invariant systems.
• For any translation-invariant local Hamiltonian exhibiting either Anderson or many-body localization, an arbitrarily small translation-invariant random local perturbation almost surely leads to the following manifestations of delocalization: (i) Transport: For any (inhomogeneous) initial state, the spatial distribution of energy or any other local conserved quantity becomes uniform at late times.