Title: Ergodicity, entanglement, and many-body localization
Abstract: Statistical mechanics is a powerful framework for describing the properties of many-particle systems, which rests on the ergodicity postulate. Surprisingly, the assumption of ergodicity breaks down in a class of disordered quantum many-body systems, via a mechanism known as many-body localization (MBL). Thus, MBL systems cannot be described using statistical mechanics. MBL phase shows a new kind of robust emergent integrability, which allows us to predict many of its properties, such as logarithmically slow spreading of quantum information. Another, even more counterintuitive property of MBL systems is that they may avoid heating under periodic driving. I will discuss that this property opens up a window for having distinct non-equilibrium phases of matter, and show several examples of such phases. I will conclude by discussing experiments and challenges for the search for non-ergodic phases and harnessing their properties for creating new kinds of non-equilibrium states.