Merging GW and dynamical mean field theory

The local density approximation (LDA) plus dynamical mean field theory (DMFT) approach has been a big step forward in describing correlated materials. However, there are two severe shortcomings: (i) the screened Coulomb interaction is usually considered to be an adjustable parameter in LDA+DMFT and (ii) the so-called double counting problem, i.e., it is very difficult to avoid counting the same correlations in LDA and DMFT twice. These shortcomings can be overcome by substituting LDA by a diagrammatic approach, for instance the so-called $GW$ approximation, where the self-energy is approximated using the random phase approximation. In the first funding period, we have implemented a non-self-consistent GW+DMFT algorithm and applied it to testbed materials of the research unit. We have developed an improved scheme to calculate the screened Coulomb interaction needed for DMFT, i.e., all screening processes are included except for the local screening within the (correlated) target orbitals, which are later treated by DMFT. The main goal of the second-funding period is the implementation of a fully self-consistent GW+DMFT algorithm, including the full frequency dependence of the screened Coulomb interaction. We also aim at a more thorough self- consistency in the GW itself, which, for solids, is hitherto only achieved within the Schilfgaarde-Kotani ``quasi- particle`` GW simplification. The selfconsistent GW+DMFT algorithm will be applied to materials for which the non-local exchange is important.

During the last few years conventional band-structure calculations in the local density approximation (LDA) have been merged with a modern many-body approach, the dynamical mean-field theory (DMFT), into a novel computational method referred to as LDA+DMFT. While this framework has proved to be a breakthrough for the realistic modeling of the electronic, magnetic, and structural properties of materials such as transition metals and their oxides, it still needs to be considerably advanced to be able to treat increasingly complex systems. This requires, for example, an improvement of the interface between the band structure and many-body constituents of the approach, the refinement and integration of efficient quantum impurity solvers, the realistic computation of free energies and forces, and the development of schemes to treat non-local correlations.The goal of the Research Unit FOR 1346 is to develop the dynamical mean-field approach into a comprehensive computational scheme for the investigation of materials with strong electronic correlations. To this end it brings together experts in electronic band structure theory, materials science, many-body approaches, quantum impurity solvers, and numerical optimization techniques. The Research Unit FOR 1346 coordinates the development of electronic structure calculations based on dynamical mean-field approaches within the German speaking part of Europe and is the first concerted research activity in this field worldwide. The goal of the Austrian subproject is, in particular, the combination of the so-called GW approach which includes non-local exchange and the DMFT which accounts for local correlations.