Avoiding Ergodicity: Static and Dynamical Localization in Clean Interacting Systems

The many body localized phase provides the rst and only example of a generic quantum inter-

acting system that does not reach thermal equilibrium, and thereby violates the most fundamental

principles of statistical physics. In the last decade, an enormous theoretical effort was invested in

understanding the nature of this phase. It has attracted a similar deal of attention also within the

experimental community, as it has the potential of storing information about initial states for long

times and it allows the application of driving protocols without heating the system to an infinite

temperature.

A key ingredient for achieving the MBL phase is randomness. The roots of this phase lie within the

phenomenon of Anderson localization, where non-interacting particles form a localized non-ergodic

phase. It is the question regarding the fate of Anderson localization in the presence of interactions

that plants the seed for the discovery of the MBL phase.