Verknüpfung Dynamischer Molekularfeldtheorie mit funktionaler Renormierungsgruppe

01/09/2017 to 31/08/2020

The theoretical description of correlated electron systems beyond the perturbative regime represents one of the main challenges for the forefront research in condensed matter physics. In fact, the impressively fast progress in the experimental engineering of correlated electron properties from bulk systems down to the nanoscale is not fully balanced yet by corresponding advances in the theoretical tools to describe them. This project aims at filling this gap with the algorithmic implementation of a novel scheme recently proposed by the applicants in [Phys. Rev. Lett. 112, 196402 (2014)], consisting in the combination of two of the most successful quantum many-body methods: the dynamical mean field theory (DMFT) and the functional renormalization group (fRG). In spite of their success, in fact, both methods have significant limitations: due to its mean-field description, DMFT neglects all non-local spatial correlations, while it captures the local part of the electronic correlations which drive, e.g., the Mott metal-insulator transitions. In contrast, the non-local correlations can be efficiently tackled by the fRG, whose application is, however, typically limited to the pertubative regime of weak electronic correlations. Our novel approach, coined DMF2RG, aims at overcoming the restrictions of both, by using the DMFT solution as starting point of the fRG treatment. This way, local - and possibly strong - correlations are fully taken into account from the very beginning within DMFT, while non-local correlations will be systematically included through the fRG procedure. By exploiting the complementary strengths of the existing state-of-the-art approaches, the DMF2RG represents a breakthrough for the theory of correlated electrons and its applications. The proposed project includes an efficient algorithmic implementation of the DMF2RG idea, its benchmarking against other methods and limiting cases and, finally, its application to prototype models and realistic systems. In particular, we aim at providing a new insight on the competing physical mechanisms at work in systems of high scientific interests, such as the pseudogap phases of lightly doped Mott insulators, unconventional superconductors and systems of adatoms on semiconducting surfaces. A long-term perspective is the multi-orbital implementation of the DMF2RG in view of a broad application of our new method by the whole solid state physics community.