DMF2RG - Merging of dynamical mean-field theory and functional renormalization group
The treatment of electronic correlations beyond the perturbative regime represents one of the main challenges in quantum many-body theory. The quest for an improvement over the state-of-the-art approaches is also motivated by the impressive progress in the experimental engineering of correlated electronic properties down to the nanoscale. This project aims at the algorithmic implementation and physical application of a novel scheme for an unbiased and non-perturbative treatment of strongly correlated fermions recently introduced by the applicants in [Phys. Rev. Lett. 112, 196402 (2014)]. The proposed idea consists in the combination of two of the most successful quantum many-body methods: dynamical mean field theory (DMFT) and functional renormalization group (fRG). DMFT captures non-perturbatively the local part of the electronic correlations which drive, e.g., the Mott-Hubbard physics, but it neglects all non-local spatial correlations. These, in turn, can be efficiently tackled by fRG, which describes the evolution from a solvable initial problem to the problem of interest, through an exact functional flow equation. The approximations introduced in practical implementations, however, limit the applicability of the fRG to the weak-coupling regime.
The novel approach, coined DMF2RG, aims at overcoming the restrictions of both, by using the DMFT solution for the local electronic self-energy and vertex function as starting point of the fRG flow. 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 flow. By exploiting the complementary strengths of the existing 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. The realization of these goals will require significant work both on the conceptual as well as on the algorithmic side. Specifically, in the first part of the project, different cutoff and truncation schemes for the DMF2RG flow will be tested, and efficient momentum/frequency parametrizations of the vertex functions will be developed. The implementation and the extension to long-range interactions will allow for various applications. In particular, we aim at providing an unbiased analysis of the competing fluctuations in the pseudogap phases of lightly doped Mott insulators, in unconventional superconductors and in systems of adatoms on semiconducting surfaces. A long-term perspective, beyond the time-frame of the project, will be the multi-orbital implementation of the DMF2RG for its broad application to realistic systems.
Project leader: Alessandro Toschi
Funding institution: 
Austrian Science Fund
Project number: I 2794-N35
Project duration: January 2017 - December 2019