Efficient Fermionic One-Loop RG for the 2D Hubbard Model at Van Hove Filling

TL;DR

This paper introduces an efficient parametrization of the four-point vertex function in the one-loop fermionic RG scheme, improving computational efficiency and reducing ambiguity in boson field introduction for the 2D Hubbard model at Van Hove filling.

Contribution

It presents a new vertex parametrization based on fermion bilinears and exchange bosons, enhancing efficiency and clarity in fermionic RG calculations.

Findings

More efficient than previous N-patch schemes

Reduces ambiguity in boson field introduction

Successfully applied to the 2D Hubbard model with a novel regularization

Abstract

We propose a novel 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. Besides being more efficient than previous N-patch schemes, this parametrization also reduces the ambiguity of introducing boson fields. We apply this parametrization to the two-dimensional (t,t')-Hubbard model using a novel $\Omega$-frequency regularization.