Channel-decomposed renormalization group equations for the vertex in a superconductor

We study ground state properties of the attractive Hubbard model at weak coupling with the aim of finding an efficient description of the effective Nambu two-particle vertex in a singlet superconductor. We decompose the vertex into a sum of interaction channels, each capturing a particular singular dependence on external momenta and frequencies. Using the functional renormalization group, we derive flow equations for the interaction channels on one-loop level. We compute the frequency dependence of the self-energy as well as the momentum and frequency dependence of the two-particle vertex. Our results for the impact of fluctuations on the superconducting gap are in good agreement with the literature. This indicates that the channel-decomposition scheme indeed captures the singular momentum and frequency dependence of the vertex.