Efficient Parametrization of the Vertex Function, $\mathrm{\Omega }$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling

We propose a new parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons. The numerical computation of the RG flow of the boson propagators reproduces the leading weak coupling instabilities of the two-dimensional Hubbard model at Van Hove filling, as they were previously obtained by a temperature RG flow. Instead of regularizing with temperature, we here use a soft frequency $\mathrm{\Omega }$-regularization that likewise does not artificially suppress ferromagnetism. Besides being more efficient than previous N-patch schemes, this parametrization also reduces the ambiguities in introducing boson fields.