The (extended) dynamical mean field theory combined with the   two-particle irreducible functional renormalization-group approach as a tool   to study strongly-correlated systems
  We propose new approach for treatment of local and non-local interactions in correlated electronic systems, which uses self-energy and the two-particle irreducible vertices, obtained from (extended) dynamical mean-field theory, as an input of two-particle irreducible functional renormalization-group (2PI-fRG) approach. Using 2PI-fRG approach allows us to treat both, local and non-local interactions. In case of purely local interaction the corresponding equations have similar (although not identical) structure to the earlier developed DMF$^2$RG approach. In a simplest truncation, neglecting scale-dependence of the two-particle irreducible vertices, we reproduce the results for the two-particle vertices/susceptibilities in the ladder approximation of the dual boson or D$\Gamma$A approach; in more sophisticated truncations the method allows us to consider non-local corrections to the self-energy, as well as the interplay of charge- and spin correlations. treatment of vertex renormalizations. The proposed scheme is tested on the two-dimensional standard and extended $U$-$V$ half-filled Hubbard models. For the standard Hubbard model we obtain non-local self-energy, which is in agreement with numerical studies; for the extended Hubbard model we obtain the boundary of charge instability, which agrees well with the results of the dual boson (DB) approach. We also find that the effect of spin correlations on electron interaction in the charge channel, not considered previously in the DB approach, only slightly reduces critical next-nearest-neighbor interaction of charge instability of the extended Hubbard model at the considered finite small temperature, yielding better agreement with dynamic cluster approximation. The considered method is rather general and can be applied to study various phenomena in strongly-correlated electronic systems. 
A. A. Katanin
cond-mat.str-el