Dynamical Signatures of Strongly Correlated Topological Phases of Matter

近年来，物质强相关拓扑相的理论研究产生了丰富多样的新物理学。然而，由于解析方法的不适用性和数值方法的高计算量，该领域对二维系统的研究大多集中在这些状态的平衡性质上。在实验方面，人工规范场的超冷原子光学晶格工程为在这些系统中实现物质的拓扑相铺平了道路。为了在实验中检测它们的拓扑性质，关于这些状态的动力学知识是一个至关重要的因素。在这个项目中，我们建议采用一种新的量子态时间演化算法来研究所谓的分数陈氏绝缘体在现实模型中的动力学行为，这些模型可能在超冷原子系统中实现。我们的目标是确定允许通过在实验室框架中可测量的动态特性识别这些强相关拓扑状态的签名。除了直接的实验相关性外，这些研究将揭示具有分数化激发的相的量子动力学的基本有趣问题。

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.