Dmitry Abanin (U. Geneva)
Ergodicity breakdown, entanglement, and non-equilibrium quantum matter

We are used to describing systems of many particles by statistical mechanics, and expect a system initially prepared in a non-equilibrium state to reach thermal equilibrium. However, the basic postulate of statistical mechanics - ergodicity -- breaks down in many-body localized systems, where disorder prevents particle transport and thermalization. I will review the current theoretical understanding of many-body localization (MBL), based on the insights from quantum entanglement. Surprisingly, highly excited MBL obey so-called area law, typical of ground states in gapped systems. This property is closely related to the new form of integrability found in MBL systems. Turning to applications, MBL persists in a class of periodically driven (Floquet) many-body systems, which opens the door to distinct Floquet phases with unusual properties such as chiral edge states at high temperature. I will discuss other recently discovered mechanisms of avoiding, or significantly slowing down thermalisation in quantum systems, including quantum many-body scars and Floquet prethermalization. I will close by discussing experimental advances and outstanding challenges in exploring ergodicty and its breakdown in quantum many-body systems.