Emerging integrability in disordered quantum systems

Antonello Scardicchio (ICTP, Trieste)

I will review some recent works which show how, in the many-body localized phase of a disordered quantum system and in perturbation theory in interaction, integrals of motion emerge which freeze the dynamics and stop ergodicity. While this picture is valid for a generic lattice system in one spatial dimension, it needs to be modified and can eventually break down for higher dimensionality and in the presence of non-abelian symmetries.