# Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point

## Abstract

We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.

- Authors:

- Russian Academy of Sciences, Miheev Institute of Metal Physics, Ural Branch (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22472215

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Experimental and Theoretical Physics

- Additional Journal Information:
- Journal Volume: 120; Journal Issue: 6; Other Information: Copyright (c) 2015 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7761

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; FERMIONS; GREEN FUNCTION; HUBBARD MODEL; IRREDUCIBLE REPRESENTATIONS; MEAN-FIELD THEORY; RENORMALIZATION

### Citation Formats

```
Katanin, A. A., E-mail: katanin@mail.ru.
```*Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point*. United States: N. p., 2015.
Web. doi:10.1134/S1063776115050039.

```
Katanin, A. A., E-mail: katanin@mail.ru.
```*Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point*. United States. https://doi.org/10.1134/S1063776115050039

```
Katanin, A. A., E-mail: katanin@mail.ru. Mon .
"Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point". United States. https://doi.org/10.1134/S1063776115050039.
```

```
@article{osti_22472215,
```

title = {Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point},

author = {Katanin, A. A., E-mail: katanin@mail.ru},

abstractNote = {We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.},

doi = {10.1134/S1063776115050039},

url = {https://www.osti.gov/biblio/22472215},
journal = {Journal of Experimental and Theoretical Physics},

issn = {1063-7761},

number = 6,

volume = 120,

place = {United States},

year = {2015},

month = {6}

}