scholarly journals Quantitative functional renormalization group description of the two-dimensional Hubbard model

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Cornelia Hille ◽  
Fabian B. Kugler ◽  
Christian J. Eckhardt ◽  
Yuan-Yao He ◽  
Anna Kauch ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Hubbard Model ◽  
Two Dimensional ◽  
Functional Renormalization Group

FUNCTIONAL RENORMALIZATION GROUP IN THE 2D HUBBARD MODEL

2006 ◽  
Vol 20 (19) ◽  
pp. 2636-2646 ◽  
Author(s):  
CARSTEN HONERKAMP
Keyword(s):  
Renormalization Group ◽  
Hubbard Model ◽  
Fermi Liquid ◽  
Broken Symmetry ◽  
Two Dimensional ◽  
Functional Renormalization Group ◽  
Recent Developments ◽  
Dimensional Models ◽  
Low Dimensional

We review recent developments in functional renormalization group (RG) methods for interacting fermions. These approaches aim at obtaining an unbiased picture of competing Fermi liquid instabilities in the low-dimensional models like the two-dimensional Hubbard model. We discuss how these instabilities can be approached from various sides and how the fermionic RG flow can be continued into phases with broken symmetry.

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

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Agnese Tagliavini ◽  
Cornelia Hille ◽  
Fabian Kugler ◽  
Sabine Andergassen ◽  
Alessandro Toschi ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Hubbard Model ◽  
Two Dimensional ◽  
Response Functions ◽  
Functional Renormalization Group ◽  
Self Energy ◽  
Numerical Effort ◽  
Physical Response ◽  
The Common ◽  
Made In

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 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 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.

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