Frequency-dependent vertex functions of the (t,t′) Hubbard model at weak coupling

Abstract

We present a functional renormalization group calculation for the two-dimensional (t,t')-Hubbard model at Van Hove filling. Using a channel decomposition we describe the momentum and frequency dependence of the vertex function in the normal phase. Compared to previous studies that neglect frequency dependences we find higher pseudo-critical scales and a smaller region of d-wave superconductivity. A large contribution to the effective interaction is given by a forward scattering process with finite frequency exchange. We test different frequency parameterizations and in a second calculation include the frequency dependence of the imaginary self-energy. We also generalize the channel decomposition to frequency-dependent fermion-boson vertex functions.