Interacting and Driven Topological States: Dynamical Mean-Field Study

我们将研究具有合成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Kagome晶格上与通量和自旋轨道耦合相互作用的费米子，三维弱和强拓扑绝缘子，以及多味拓扑绝缘子。我们还将研究密度相关规范场对二维晶格拓扑带的影响，如果我们期望奇异的莫特绝缘子状态。在实验相关的准周期和准晶体光学晶格几何形状以及光学散斑无序存在下，将评估在猝灭无序存在下相互作用拓扑态的稳定性，我们还将寻找拓扑Anderson绝缘体相。我们的研究基于非微扰动力学平均场理论（DMFT）及其对非齐次系统、时间周期驱动系统和开放量子点阵系统的适应性。在周期性驱动、相互作用的Floquet系统中，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，并研究加热效应和能量耗散。这也包括具有跳变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。对于与环境耦合的开放、相互作用的二维费米子晶格系统，我们将确定多体陈恩数，研究拓扑邻近效应，以及通过适当选择耗散来稳定陈恩绝缘子的可能性。我们将进一步开发在二维和三维光学晶格实验中测量强相关费米子拓扑不变量的方案，并将其与基于DMFT和有效拓扑哈密顿量的定量预测相结合。

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.