Many-body localization

Abstract

A system of interacting degrees of freedom in the presence of disorder hosts a variety of fascinating phenomena. Disorder itself has led to the striking phenomena of localization of classical waves and non-interacting quantum mechanical particles. There are even phase transitions (like the glass transition) which are driven largely due the effects of disorder. The work in this dissertation primarily addresses the interplay of interactions and disorder for the fate of ergodicity in classical and quantum systems. We specifically question the assumption of ergodicity in a generic, isolated spin-system with interactions and disorder in the absence of coupling to an external heat bath. Our results predict the existence of a novel phase transition at finite temperature (even at `infinite' temperature) in the quantum regime driven by the strength of disorder. At relatively low disorder in the ergodic phase, an isolated quantum system can serve as its own heat bath allowing any subsystem to thermalize. While at strong disorder due to the localization of excitations, the isolated system fails to serve as a heat bath. In the limit of infinite system size, there is a quantum phase transition between the two phases with the critical point showing infinite-randomness like scaling properties. Based on our conventional understanding, the low frequency dynamics of quantum systems at finite temperature are often describable in terms of an effective classical model. With this motivation in mind, we also studied the dynamics of an interacting, disordered classical spin-model. Our results exclude the possibility of many-body localization in classical systems. A classical many-body system at strong enough disorder becomes chaotic under the dynamics of its own hamiltonian thus converging to thermal equilibrium at long times. Hence, many-body localization is a macroscopic quantum phenomenon at extensive energies without a classical counterpart.