Many-Body Localization: integrability, glassiness, and fluctuation-driven transitions

Many-Body Localization (MBL) is a peculiar form of ergodicity breaking and out-of-equilibrium dynamics which occurs in certain interacting quantum systems subject to quenched disorder. In the first part of this talk, I will briefly discuss the connection between localization, integrability and glassiness, in order to motivate the claim that Many-Body Localized systems are both integrable and glassy, albeit in their own special way. In the second part of the talk, I will discuss a toy model to capture the interplay between quenched disorder leading to localisation and slow, thermally induced fluctuations affecting the effective local disorder of the system. I will summarise the rich phenomenology brought about by these additional fluctuations, stressing in particular the connections to the unfreezing transition and configurational chaos in the simplest models of glassy systems. This part is based on joint work with Markus Mueller.

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