Dynamical Signatures of Strongly Correlated Topological Phases of Matter

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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.