Many-body localization in the disordered Fermi-Hubbard model

Abstract:  How isolated quantum systems reach thermal equilibrium is a long-standing question of continuing interest. The absence of equilibration in some systems is also well known, notably Anderson localization in noninteracting systems with quenched disorder.  However, it has only relatively recently been understood that the absence of equilibration can persist in the presence of interactions, dubbed many-body localization.  While most of the theoretical work in this area has focused on spin systems, in which there is just one local degree of freedom, systems with multiple coupled degrees of freedom are of interest, not least because most experimental studies of many-body localization use cold atoms described by the Hubbard model. This talk will review this context and explore the specific case of the disordered Fermi-Hubbard model.  With two coupled local degrees of freedom, charge and spin, how does disorder in one of these influence localization in the other? Writing the Hamiltonian in terms of charge- and spin-specific integrals of motion, we extract time scales associated with charge-charge, spin-spin, and charge-spin coupling and connect these with the growth of entanglement.