Interacting and Driven Topological States: Dynamical Mean-Field Study

点击翻译按钮获取中文摘要

We will investigate topological many-body states of interacting quantum gases in two- and three- dimensional optical lattice systems with synthetic gauge fields. This includes interacting fermions with flux and spin-orbit coupling on the Kagome lattice, three-dimensional weak and strong topological insulators, and multiflavor topological insulators. We will also investigate the effect of density-dependent gauge fields on topological bands in two-dimensional lattices, were we expect exotic Mott-insulator states. The stability of interacting topological states in the presence of quenched disorder will be evaluated for experimentally relevant quasiperiodic and quasicrystalline optical lattice geometries and in the presence of optical speckle disorder, and we will also search for topological Anderson insulator phases. Our studies are based on the nonperturbative Dynamical Mean-Field Theory (DMFT) and its adaptations to inhomogeneous systems, to time-periodically driven systems, and to open quantum lattice systems. In periodically driven, interacting Floquet systems, corresponding to realizations of synthetic gauge fields by driven optical lattices, which are additionally coupled to a heat bath, we will search for topological nonequilibrium steady states, develop suitable generalized invariants to characterize them, and investigate heating effects and energy dissipation. This also includes lattice systems with double modulation of hopping and interaction, which can yield Floquet realizations of density-dependent gauge fields. For open, interacting two-dimensional fermionic lattice systems coupled to an environment, we will determine the many-body Chern number and investigate topological proximity effects, as well as the possible stabilization of Chern insulators by suitable choice of dissipation. We will furthermore develop protocols for measuring topological invariants of strongly correlated fermions in experiments with two- and three-dimensional optical lattices, and combine them with quantitative predictions based on DMFT and the effective topological Hamiltonian.