Non-local correlations out of equilibrium

相互作用系统中的拓扑量子现象和时间分辨光谱学的最新突破对多体理论提出了新的挑战：时空电子相关性经常强烈影响拓扑和动态材料特性，但同时也阻碍了实验的明确解释，更不用说对材料特性的可靠定量预测了。这个研究单位QUAST（相关电子物质的定量时空模型构建）旨在通过理论方法开发和协调实验的协调努力来解决这一挑战：我们的中心目标是发展一个电子结构理论，解释时空电子相关性，最终解释和定量建模相关材料中的拓扑和动态现象。将不同的长度和时间尺度与电子相关性和拓扑结构交织在一起所产生的复杂性需要相关系统、拓扑结构和非平衡动力学方面的专家团队的密切合作，例如QUAST的工作。该计划中的研究小组将在近似、抽象和时空特征的互补水平上发展理论ansätze，以生成基准工具的共同平台。我们的研究议程涵盖了从更接近但部分已经具有实际意义的方法（如GW+EDMFT， DFT+TPSC或DFT+SBT）到最准确但目前更基于模型的方法（如DGammaA，双费米子/玻色子或量子簇理论）。我们想要回答的常见问题是：如何描述和预测交互系统中的拓扑结构？如何定量描述相互作用诱导的物质拓扑状态和相关系统中的动态过程？如何通过定量建模和泵-探针实验相结合来解开相关现象？如何引导相关电子系统进入新的物质非平衡状态？如何处理动态、拓扑和相关性的相互作用？为此，我们将重点关注一组演示模型（扩展Hubbard，周期Anderson和拓扑模型）和试验台材料（Ce3Bi4Pd3， WTe2和TaS2 (X=S,Se)）与嵌入QUAST的三个实验组合作。理论方法将是先进的，相互之间和与实验交叉检查，连接到拓扑概念，并推广到非平衡和动态现象。对于上述试验台材料，将在第一个资助期内实施从最短的原子时空尺度到最长的完整模拟链，并与实验进行严格比较。在第二个资助期，我们的目标是使上述方法达到成熟水平，从而建立一个平台，用于在广泛的相关系统中可靠地建模和设计动态和拓扑现象。

Topological quantum phenomena in interacting systems and recent breakthroughs in time-resolved spectroscopy pose a new challenge for many-body theory: Spatio-temporal electronic correlations often strongly impact topological and dynamical material properties but at the same time hinder an unambiguous interpretation of experiments, let alone a reliable quantitative prediction of material properties. This research unit QUAST (Quantitative spatio-temporal model-building for correlated electronic matter) aims at addressing this challenge by a coordinated effort in theoretical method development and concerted experiments: Our central goal is to develop an electronic structure theory accounting for spatio-temporal electronic correlations to ultimately explain and quantitatively model topological and dynamical phenomena in correlated materials.The complexity resulting from intertwining different length- and time-scales with electronic correlations and topology requires a close cooperation of a team of experts in correlated systems, topology and non-equilibrium dynamics, such as the QUAST effort. The research groups in this initiative will develop theoretical ansätze at complementary levels of approximation, abstraction, and spatio-temporal character in order to generate a common platform of benchmarked tools. Our research agenda spans from more approximate but in parts already material realistic approaches (such as GW+EDMFT, DFT+TPSC or DFT+SBT) to the most accurate but currently more model-based methods (e.g. DGammaA, dual fermions/bosons or quantum cluster theories).Pressing common open questions we want to answer are: How can topology in interacting systems be characterized and predicted? How to quantitatively describe interaction-induced topological states of matter and dynamical processes in correlated systems? How to disentangle correlation phenomena by linking quantitative modelling and pump-probe experiments? How to steer correlated electron systems into novel non-equilibrium states of matter? How to tackle the interplay of dynamics, topology and correlations?For that we will focus on a set of demonstrator models (extended Hubbard, periodic Anderson and topological models) and testbed materials (Ce3Bi4Pd3, WTe2 and TaS2 (X=S,Se)) in collaboration with three experimental groups embedded in QUAST.The theoretical methods will be advanced, cross-checked among each other and with experiments, linked to topological concepts, and generalized to non-equilibrium and dynamical phenomena. For the testbed materials above, a full simulation chain from shortest atomic spatio-temporal scales to longest ones with rigorous comparisons to experiments will be implemented in the first funding period. In the second funding period we aim at bringing the aforementioned approaches to a level of maturity that allows for the establishment of a platform for reliable modeling and design of dynamical and topological phenomena in a broad class of correlated systems.