Approximating the frequency dependence of the effective interaction in the functional renormalization group for many-fermion systems

TL;DR

This paper introduces an efficient approximation method for the frequency dependence of interactions in the functional renormalization group, enabling more precise analysis of many-fermion systems like the 2D Hubbard model.

Contribution

It proposes a new parametrization of the frequency dependence that reduces computational complexity while maintaining accuracy, validated on Cooper pairing and the 2D Hubbard model.

Findings

The approximation accurately captures the frequency dependence in Cooper pairing.

Application to the 2D Hubbard model demonstrates practical effectiveness.

The method reduces numerical effort significantly.

Abstract

The functional renormalization group has become a widely used tool for the analysis of the leading low-temperature correlations in weakly to moderately coupled many-fermion lattice systems. A bottleneck for quantitatively more precise results is that the treatment of the frequency dependence of the flowing interactions is numerically quite demanding. Yet the frequency dependence is needed to compute relevant selfenergies and hence for controlled results on the energy scales for ordering or for the quasiparticle properties. Here we explore an approximate parametrization of the frequency dependence of the interaction vertex that is inspired by established simplifications in the theory of superconductivity and that keeps the numerical effort bounded. We demonstrate the validity of the approximation for Cooper pairing problems and apply it to the two-dimensional Hubbard model.