The existing theory of quantum statistical mechanics describes open systems in contact with large reservoirs. However, experimental advances in the construction and control of isolated quantum systems have highlighted the need for an analogous theory of isolated systems. It has been realized that isolated quantum systems can support behavior which has no analog in open quantum systems. A prominent example is the phenomenon of many body localization.
Many body localization occurs in isolated quantum systems, usually with strong disorder, and is marked by absence of dissipation, absence of thermal equilibration, a strictly zero DC conductivity (even at energy densities corresponding to high temperatures), and a memory of the initial conditions that survives in local observables for arbitrarily long times. Recently, my co-workers and I have demonstrated that many body localization also opens the door to new states of matter which cannot exist in thermal equilibrium, such as topological order at finite energy density, or broken symmetry states below the equilibrium lower critical dimension. In this talk, I review the essential features of the many body localization phenomenon, present our recent work on localization protected order, and provide a survey of open problems. I also present my ongoing work seeking to make contact between the theory and experiments, and discuss potential technological applications of these ideas.
I received my PhD from MIT in 2012, working in the field of theoretical quantum physics. My thesis advisor was Leonid Levitov, and my thesis was entitled `Quantum many body physics in single and bilayer graphene.' In the course of my PhD I conducted research on numerous aspects of quantum many body physics in low dimensional systems, motivated chiefly by experiments conducted in the group of Amir Yacoby. In fall 2012 I began a postdoctoral fellowship at the Princeton Center for Theoretical Science (PCTS). While I have continued to work on graphene and related Dirac fermion materials (such as topological insulators and Weyl semimetals), I have also developed a keen interest in disordered systems. A particularly rich set of problems in the field of disordered systems is associated with the phenomenon of many body localization. Problems connected with many body localization have been at the core of my research effort in the course of my postdoctoral fellowship. I will present some recent progress in my talk.