Dynamical Signatures of Strongly Correlated Topological Phases of Matter

近年来，对物质强关联拓扑相的理论研究产生了丰富多样的新物理。然而，在这个领域中的二维系统的大多数调查都集中在这些状态的平衡性质，由于分析方法的不适用性和数值方法的高计算工作量。在实验方面，超冷原子与人工规范场的光学晶格工程为实现这些系统中物质的拓扑相铺平了道路。这些国家的动态知识是一个至关重要的成分，以检测其拓扑性质的实验装置。在这个项目中，我们建议采用一种新的算法的量子态的时间演化来研究所谓的分数陈绝缘体的动力学行为，在现实的模型，可以实现在超冷原子系统。这是我们的目标，以确定签名，允许识别这些强相关的拓扑状态的动力学特性，这是在实验室框架内可测量的。除了直接的实验相关性，这些研究将揭示量子动力学在分数激发阶段的基本有趣的问题。

The theoretical study of strongly correlated topological phases of matter has generated a rich variety of novel physics in recent years. However, most of the investigations for two-dimensional systems in this field have focused on equilibrium properties of these states due to the non-applicability of analytical methods and the high computational effort of numerical approaches. On the experimental side, the engineering of optical lattices for ultracold atoms with artificial gauge fields has paved the way towards the realization of topological phases of matter in these systems. The knowledge about the dynamics of these states is a crucial ingredient in order to detect their topological nature in the experimental setup. In this project, we propose to employ a novel algorithm for the time evolution of quantum states to investigate the dynamical behavior of so-called fractional Chern insulators in realistic models that may be implemented in systems of ultracold atoms. It is our goal to determine signatures that allow the identification of these strongly correlated topological states by dynamical properties which are measurable in a laboratory framework. Apart from the direct experimental relevance, the studies will shed light into the fundamentally interesting question of quantum dynamics in phases with fractionalized excitations.