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

TL;DR

This paper introduces a new efficient parametrization of the vertex function in fermionic RG schemes, accurately capturing instabilities in the 2D Hubbard model at Van Hove filling without suppressing ferromagnetism.

Contribution

It presents a novel vertex parametrization based on fermion bilinears and exchange bosons, improving computational efficiency and reducing ambiguities in boson field introduction.

Findings

Reproduces known weak coupling instabilities of the Hubbard model.

Uses a soft frequency $ ext{Omega}$-regularization avoiding suppression of ferromagnetism.

Outperforms previous N-patch schemes in efficiency.

Abstract

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 $\Omega$-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.