Efficient time evolution of quantum many-body systems in 2D with matrix product states

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The numerical study of dynamical properties in and out of equilibrium is essential for understanding the physics of strongly interacting systems. Dynamical structure factors provide for example valuable insights into the nature of new phases of matter. This is particularly important for the experimental detection of theoretically proposed spin-liquid states. Furthermore, studying the non-equilibrium dynamics allows us on the other hand to explore the ability of a system to thermalize.Simulating the real-time evolution of a strongly-interacting quantum many-body system is a very difficult task and thus requires efficient numerical algorithms. In project P3N, we will use and extend matrix-product state based time-evolution methods to tackle a number of important questions regarding the dynamics of two-dimensional quantum-many body systems.In the first part of the project, we will predict experimentally accessible fingerprints of topological order in spin liquids. For this, we will make use of a recently developed matrix-product state based algorithm for the time evolution of two-dimensional quantum systems. We will obtain dynamical spin structure factors that can be directly compared to neutron scattering experiments. In the second part, we focus on the dynamics of two-dimensional many-body localized systems. Here, we will investigate various quench protocols that are relevant for recent experiments in optical lattices. Furthermore, we will study the dynamics of entanglement and compare it to known results in one-dimensional systems. On the methodological side, we are going to develop and implement a time-evolution algorithm for tensor-product states in disordered systems.