Using the (extended) dynamical mean field theory as a starting point for the two-particle irreducible functional renormalization-group approach for strongly-correlated systems

We suggest a new approach for treatment of local and non-local interactions in correlated electronic systems, which is based on the combination of the (extended) dynamical mean-field theory ((E)DMFT) and the two-particle irreducible functional renormaliztion-group (2PI-fRG) method. The considering approach uses self-energy and the two-particle irreducible vertices, obtained from (E)DMFT, as an input of 2PI-fRG approach. Using 2PI vertices may improve the applicability of various truncations and fulfilling conservation laws in comparison with one-particle irreducible approaches. In case of purely local interaction in a certain "ladder" truncation of the DMFT+2PI-fRG equations, the obtained equation for the self-energy has a similar, although not identical, structure to that in the ladder dynamic vertex approximation (D$\Gamma $A). For the non-local interactions, in a simplest truncation we reproduce the results for the two-particle vertices/susceptibilities in the ladder approximation of the dual boson approach, but obtain different equation for the self-energy with a correct treatment of the one-particel reducible vertices of higher orders. The proposed scheme is rather general and can be applied to study various phenomena in strongly-correlated electronic systems, e.g. as a tool describing ab initio screening of the Coulomb interaction in strongly correlated systems.