A Rigorous Proof of Fermi Liquid Behavior for Jellium Two-Dimensional Interacting Fermions

TL;DR

This paper rigorously proves that two-dimensional jellium fermion systems exhibit Fermi liquid behavior at low temperatures, with bounded derivatives of the self-energy, using continuous constructive renormalization group methods.

Contribution

It provides a rigorous mathematical proof of Fermi liquid behavior for 2D jellium fermions, establishing bounded self-energy derivatives and non-perturbative transition temperatures.

Findings

Fermi liquid behavior is confirmed at low temperature.

Self-energy derivatives remain bounded, excluding Luttinger liquid.

Transition temperatures are non-perturbative in the coupling constant.

Abstract

Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains analytic in the coupling constant $\lambda$ for $|\lambda| |\log T| \le K $ where $K$ is some numerical constant and $T$ is the temperature. Furthermore in that range of parameters, the first and second derivatives of the self-energy remain bounded, a behavior which is that of Fermi liquids and in particular excludes Luttinger liquid behavior. Our results prove also that in dimension two any transition temperature must be non-perturbative in the coupling constant, a result expected on physical grounds. The proof exploits the specific momentum conservation rules in two dimensions.