Many-Body Localization: Stability and Instability

Understand

Rare regions with weak disorder (Griffiths regions) have the potential to spoil localization.

• We describe a non-perturbative construction of local integrals of motion (LIOMs) for a weakly interacting spin chain in one dimension, under a physically reasonable assumption on the statistics of eigenvalues.
• We discuss ideas about the situation in higher dimensions, where one can no longer ensure that interactions involving the Griffiths regions are much smaller than the typical energy-level spacing for such regions.
• We argue that ergodicity is restored in dimension d > 1, although equilibration should be extremely slow, similar to the dynamics of glasses.