From Quantum Many-Body Physics to Many-Body Localization in Atomic systems

Ultracold atomic systems have witnessed rapid developments in the last decade in many aspects, and has now reached a new era where quantum correlations and many-body complexity emerge in unprecedented controllable fashion. These developments stimulate unique angles to study quantum many-body physics especially in non-equilibrium aspects. Specifically, I will discuss quantum many-body localization, a dynamical quantum phase transition at infinite temperature, in optical lattices. I will describe thermalization in an isolated quantum system in the sense of eigenstate thermalization hypothesis, and its breakdown in the presence of strong disorder. I will present our work on nonergodic metallic phase that arises from coexisting localized and delocalized degrees of freedom in one dimensional incommensurate lattices. The conceptual novelty of this nonergodic metallic phase lies in that it is extended in real space but "localized" in the high-dimensional many-body Hilbert space. Numerical evidence and theoretical arguments for this novel phase will be presented.