Non-local correlations out of equilibrium

相互作用体系中的拓扑量子现象和时间分辨光谱的最新突破对多体理论提出了新的挑战：时空电子关联往往强烈地影响材料的拓扑和动力学性质，但同时也阻碍了对实验的明确解释，更不用说可靠的材料性质的定量预测了。这个研究单位QUAST(相关电子物质的定量时空建模)旨在通过理论方法开发和协同实验的协调努力来应对这一挑战：我们的中心目标是发展一种解释时空电子关联的电子结构理论，以最终解释和定量模拟关联材料中的拓扑和动力学现象。不同的长度和时间尺度与电子关联和拓扑交织在一起所产生的复杂性需要相关系统、拓扑和非平衡动力学方面的专家团队的密切合作，例如Quast努力。这一倡议中的研究小组将在近似、抽象和时空特征的互补水平上开发理论分析，以便生成一个基准工具的公共平台。我们的研究议程从更接近但部分已经是物质现实的方法(如GW+EDMFT，DFT+TPSC或DFT+SBT)到最精确但目前更基于模型的方法(例如DGammaA，双费米子/玻色子或量子团簇理论)。我们想要回答的常见公开问题是：如何表征和预测相互作用系统中的拓扑？如何定量描述相互作用引起的物质拓扑态和关联系统中的动力学过程？如何通过将定量模型和泵浦-探测实验联系起来来解开关联现象？如何引导相关电子系统进入物质的新的非平衡状态？如何处理动力学、拓扑和关联的相互作用？为此，我们将与QUAST中的三个实验小组合作，重点介绍一组演示模型(扩展的Hubbard模型、周期Anderson模型和拓扑模型)和实验床材料(Ce3Bi4Pd3、WTe2和TaS2(X=S，Se))。理论方法将得到改进，相互验证，并与实验相互验证，与拓扑概念相联系，并推广到非平衡和动力学现象。对于上述试验台材料，将在第一个资助期内实施从最短原子时空尺度到最长原子时空尺度的完整模拟链，并与实验进行严格的比较。在第二个资助期，我们的目标是使上述方法达到成熟的程度，以便建立一个平台，在广泛的相关系统中对动力和拓扑现象进行可靠的建模和设计。

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.