Functional renormalization-group approaches, one-particle (ir)reducible with respect to local Green functions, using the dynamical mean-field theory as a starting point

We consider formulations of the functional renormaliztion-group flow for correlated electronic systems, having the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting the one-particle irreducible (with respect to the local Green functions) six-point vertices and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF$^{2}$RG approach [Phys. Rev. Lett. 112, 196402 (2014)], but also by the scale-dependent generalization of the one-particle irreducible (with respect to local Green functions, 1PI-LGF) representation of the generating functional [Phys. Rev. B 88, 115112 (2013)]. The second class is represented by the fRG flow within the dual fermion (DF) approach [Phys. Rev. B 77, 033101 (2008); ArXiv 1411.1342]. We compare formulations of fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.