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Many body localization occurs in isolated quantum systems, usually with strong disorder, and is marked by absence of dissipation, absence of thermal equilibration, and a memory of the initial conditions that survives in local observables for arbitrarily long times. The many body localized regime is a far from equilibrium, strongly disordered regime that constitutes a new frontier for quantum statistical mechanics. Recently, my co-workers and I have demonstrated that many body localization opens the door to new states of matter which cannot exist in thermal equilibrium, such as topologically ordered states without a bulk gap, and broken symmetry states at high energy densities in one dimension. We have also uncovered a host of unexpected properties, such as a set of universal spectral features and a non-local charge response, that have striking implications for fields as diverse as quantum Hall based quantum computation and quantum control. In this talk, I review the essential features of the many body localization phenomenon, and present some of the recent progress that has been made in this field. I also discuss the implications of these results for both theory and experiment, and the connections with diverse areas of theoretical physics. I conclude with a discussion of future directions.
Reference: Rahul Nandkishore and David A. Huse, arXiv: 1404.0686 [Annual Reviews of Condensed Matter Physics, 2015]