Interacting and Driven Topological States: Dynamical Mean-Field Study

我们将研究具有人工规范场的二维和三维光学晶格系统中相互作用量子气体的拓扑多体态。这包括在可果美晶格上具有通量和自旋轨道耦合的相互作用费米子，三维弱和强拓扑绝缘体，以及多味拓扑绝缘体。我们还将研究密度依赖规范场对二维晶格中拓扑带的影响，我们期望奇异的莫特绝缘体状态。相互作用的拓扑状态的稳定性在淬火无序的存在下，将评估实验相关的准周期和准晶光学晶格几何形状和在存在的光学散斑的障碍，我们也将寻找拓扑安德森绝缘体阶段。我们的研究是基于非微扰动力学平均场理论（DMFT）及其对非均匀系统，时间周期驱动系统和开放量子晶格系统的适应性。在周期性驱动，相互作用的Floquet系统，对应于实现的合成规范场的驱动光学晶格，这是另外耦合到一个热浴，我们将寻找拓扑非平衡稳态，开发合适的广义不变量来表征它们，并调查加热效应和能量耗散。这也包括具有跳跃和相互作用双重调制的晶格系统，它可以产生密度依赖规范场的Floquet实现。对于开放的，相互作用的二维费米子晶格系统耦合到一个环境中，我们将确定多体陈数和研究拓扑邻近效应，以及可能的稳定陈绝缘体通过适当的选择耗散。我们将进一步开发在实验中测量强关联费米子的拓扑不变量的协议与二维和三维光学晶格，并将它们与基于DMFT和有效拓扑哈密顿量的定量预测联合收割机。

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.