Non-local correlations out of equilibrium

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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.