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We consider formulations of the functional renormaliztion-group flow forcorrelated electronic systems, having the dynamical mean-field theory as astarting point. We classify the corresponding renormalization-group schemesinto those neglecting the one-particle irreducible (with respect to the localGreen functions) six-point vertices and neglecting one-particle reduciblesix-point vertices. The former class is represented by the recently introducedDMF$^{2}$RG approach [Phys. Rev. Lett. 112, 196402 (2014)], but also by thescale-dependent generalization of the one-particle irreducible (with respect tolocal Green functions, 1PI-LGF) representation of the generating functional[Phys. Rev. B 88, 115112 (2013)]. The second class is represented by the fRGflow within the dual fermion (DF) approach [Phys. Rev. B 77, 033101 (2008);ArXiv 1411.1342]. We compare formulations of fRG approach in each of thesecases and suggest their further application to study 2D systems within theHubbard model.

journal of experimental and theoretical physics

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