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

平衡态和非平衡态动力学性质的数值研究对于理解强相互作用系统的物理性质是必不可少的。例如，动力学结构因子提供了对物质新相性质的有价值的见解。这对于理论上提出的自旋液体状态的实验检测特别重要。此外，研究非平衡动力学另一方面可以让我们探索系统的热化能力。模拟强相互作用量子多体系统的实时演化是一项非常困难的任务，因此需要高效的数值算法。在P3N项目中，我们将使用和扩展基于矩阵乘积态的时间演化方法来解决一些关于二维量子多体系统动力学的重要问题。在项目的第一部分，我们将预测自旋液体中实验可获得的拓扑有序指纹。为此，我们将利用最近开发的基于矩阵乘积状态的算法来计算二维量子系统的时间演化。我们将获得动态自旋结构因子，可以直接与中子散射实验进行比较。在第二部分中，我们主要研究二维多体定域系统的动力学。在这里，我们将研究各种淬火协议，是相关的最近的实验在光学晶格。此外，我们将研究纠缠的动力学，并将其与一维系统中的已知结果进行比较。在方法论方面，我们将开发和实现无序系统中张量积状态的时间演化算法。

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.