Dynamics of Many-Body Localization

Many-body localization is a peculiar dynamical transition between ergodic and non-ergodic phases, which may occur at any temperature and in any dimension. Current theory suggest that for temperatures below the transition the system is non-ergodic and localized, such that conductivity vanishes at the thermodynamic limit, while for temperatures above the transition the system is thermal and conductive. In this talk I will present a study of ergodicity and dynamical properties of the many-body localization transition using a combination of non-equilibrium diagrammatic techniques and numerically exact methods. I will present the dynamical phase-diagram at infinite temperature, and provide evidence of existence of a novel phase, which is ergodic yet has a vanishing DC conductivity.