Luttinger liquid fixed point for a 2D flat Fermi surface

TL;DR

This paper demonstrates the existence of a line of non-trivial fixed points corresponding to Luttinger liquid behavior in a 2D fermionic system with a flat Fermi surface, resolving previous conflicting results.

Contribution

It provides a non-perturbative analysis showing the RG flow towards Luttinger liquid fixed points using Ward Identities, clarifying the nature of 2D flat Fermi surface systems.

Findings

Existence of a line of non-trivial RG fixed points for 2D flat Fermi surfaces.

Luttinger liquid behavior is confirmed at these fixed points.

Marginally relevant operators can lead to flow away from the fixed points.

Abstract

We consider a system of 2D interacting fermions with a flat Fermi surface. The apparent conflict between Luttinger and non Luttinger liquid behavior found through different approximations is resolved by showing the existence of a line of non trivial fixed points, for the RG flow, corresponding to Luttinger liquid behavior; the presence of marginally relevant operators can cause flow away from the fixed point. The analysis is non-perturbative and based on the implementation, at each RG iteration, of Ward Identities obtained from local phase transformations depending on the Fermi surface side, implying the partial vanishing of the Beta function.