## Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions

Agnese Tagliavini, Cornelia Hille, Fabian B. Kugler, Sabine Andergassen, Alessandro Toschi, Carsten Honerkamp

SciPost Phys. 6, 009 (2019) · published 18 January 2019

- doi: 10.21468/SciPostPhys.6.1.009
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### Abstract

We present a functional renormalization group (fRG) study of the two dimensional Hubbard model, performed with an algorithmic implementation which lifts some of the common approximations made in fRG calculations. In particular, in our fRG flow; (i) we take explicitly into account the momentum and the frequency dependence of the vertex functions; (ii) we include the feedback effect of the self-energy; (iii) we implement the recently introduced multiloop extension which allows us to sum up {\emph{all}} the diagrams of the parquet approximation with their exact weight. Due to its iterative structure based on successive one-loop computations, the loop convergence of the fRG results can be obtained with an affordable numerical effort. In particular, focusing on the analysis of the physical response functions, we show that the results become {\emph{independent}} from the chosen cutoff scheme and from the way the fRG susceptibilities are computed, i.e., either through flowing couplings to external fields, or through a "post-processing" contraction of the interaction vertex at the end of the flow. The presented substantial refinement of fRG-based computation schemes paves a promising route towards future quantitative fRG analyses of more challenging systems and/or parameter regimes.

### Cited by 6

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

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^{1 }^{2 }Agnese Tagliavini, -
^{1 }Cornelia Hille, -
^{3 }Fabian Kugler, -
^{1 }Sabine Andergassen, -
^{2 }Alessandro Toschi, -
^{4 }^{5 }Carsten Honerkamp

^{1}Eberhard Karls Universität Tübingen / University of Tübingen^{2}Technische Universität Wien / Vienna University of Technology [TUW]^{3}Ludwig-Maximilians-Universität München / Ludwig Maximilian University of Munich [LMU]^{4}Jülich Aachen Research Alliance [JARA]^{5}Rheinisch-Westfälische Technische Hochschule Aachen / RWTH Aachen University [RWTH]

- Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]