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The functional renormalization group has become a widely used tool for theanalysis of the leading low-temperature correlations in weakly to moderatelycoupled many-fermion lattice systems. A bottleneck for quantitatively moreprecise results is that the treatment of the frequency dependence of theflowing interactions is numerically quite demanding. Yet the frequencydependence is needed to compute relevant selfenergies and hence for controlledresults on the energy scales for ordering or for the quasiparticle properties.Here we explore an approximate parametrization of the frequency dependence ofthe interaction vertex that is inspired by established simplifications in thetheory of superconductivity and that keeps the numerical effort bounded. Wedemonstrate the validity of the approximation for Cooper pairing problems andapply it to the two-dimensional Hubbard model.

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