Field-theoretical renormalization group for a flat two-dimensional Fermi surface

TL;DR

This paper performs a detailed two-loop renormalization group analysis of interacting fermions on a flat two-dimensional Fermi surface, revealing new anisotropic suppression effects at moderate couplings.

Contribution

It provides the first explicit two-loop calculation of coupling functions and self-energy for this system within the field theoretical RG framework, extending previous one-loop results.

Findings

No significant change in RG flow at weak coupling compared to one-loop results.

Anisotropic suppression of quasiparticle weight Z along the Fermi surface at moderate coupling.

Renormalized coupling functions vanish for certain external momenta configurations.

Abstract

We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group (RG) approach. Throughout the calculation both the Fermi surface and the Fermi velocity are assumed to be fixed and unaffected by interactions. We show that in two dimensions, in a weak coupling regime, there is no significant change in the RG flow compared to the well-known one-loop results available in the literature. However, if we extrapolate the flow to a moderate coupling regime there are interesting new features associated with an anisotropic suppression of the quasiparticle weight Z along the Fermi surface, and the vanishing of the renormalized coupling functions for several choices of the external momenta.