Abstract

It has been the belief that generic quantum many-body systems necessarily approach thermal equilibrium after a long time evolution. As a consequence any quantum information encoded in the initial state is lost in the course of the dynamics and the late time dynamics is described by simple hydrodynamics. However, recently the generality of this assumption of ergodic evolution has been put into question. In this talk, we show how ergodicity---and with that fundamental concepts of thermodynamics---can break down in a disordered many-body system by the phenomenon of many-body localization. Many-body localization describes an exotic phase of matter in which quantum information can prevail for infinitely long times even at finite temperatures. We discuss a scenario a how many-body localized phase transitions via a slowly relaxing sub-diffusive regime to an ergodic metallic phase. Finally, we show how information and operators spread in ergodic many-body phases.