A functional generalization of the field-theoretical renormalization group approach for the single-impurity Anderson model

TL;DR

This paper develops a functional field-theoretical renormalization group approach for the single-impurity Anderson model, accurately reproducing known results and offering a potentially easier method for higher-order calculations of electronic correlations.

Contribution

It introduces a novel functional RG scheme that simplifies higher-loop calculations and accurately models the Anderson impurity problem, aligning well with existing numerical data.

Findings

Accurately reproduces numerical renormalization group data for weak to moderate interactions.

Demonstrates the method's agreement with other functional RG approaches.

Suggests the approach's potential for higher-order calculations at stronger couplings.

Abstract

We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta \emph{et al.} [Phys. Rev. Lett. \textbf{85}, 4940 (2000)], which consists of defining a soft ultraviolet regulator in the space of Matsubara frequencies for the renormalized Green's function. Then we proceed to derive analytically and solve numerically integro-differential flow equations for the effective couplings and the quasiparticle weight of the present model, which fully treat the interplay of particle-particle and particle-hole parquet diagrams and the effect of the two-loop self-energy feedback into them. We show that our results correctly reproduce accurate numerical renormalization group data for weak to slightly moderate interactions. These results are in excellent agreement with other functional Wilsonian RG works available in the literature. Since the field-theoretical RG method turns out to be easier to implement at higher loops than the Wilsonian approach, higher-order calculations within the present approach could improve further the results for this model at stronger couplings. We argue that the present RG scheme could thus offer a possible alternative to other functional RG methods to describe electronic correlations within this model.