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

TL;DR

This paper explores different functional renormalization-group schemes based on dynamical mean-field theory, classifying them by their treatment of local Green function vertices, and compares their formulations for studying 2D Hubbard models.

Contribution

It classifies and compares various fRG approaches starting from DMFT, highlighting their differences in handling local Green function vertices and suggesting applications to 2D Hubbard systems.

Findings

Comparison of DMF$^{2}$RG and 1PI-LGF approaches.

Analysis of dual fermion fRG flow.

Potential for studying 2D Hubbard models.

Abstract

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.