Interacting Fermi liquid at finite temperature: Part I: Convergent Attributions

TL;DR

This paper proves that a two-dimensional interacting Fermi system at low temperature behaves as a Fermi liquid with bounds on derivatives of the selfenergy, advancing the understanding of phase transitions in such systems.

Contribution

It establishes rigorous bounds for a 2D Fermi liquid at finite temperature using renormalization group methods, focusing on convergent contributions.

Findings

Fermi liquid behavior established for g < const/|logT|

Uniform bounds on selfenergy derivatives proven

Progress towards rigorous study of BCS transition in 2D systems

Abstract

Using the method of continuous renormalization group around the Fermi surface, we prove that a two-dimensional jellium interacting system of Fermions at low temperature T is a Fermi liquid (analytic in the coupling constant g) for g < const/|logT|, and satisfying uniform bounds on the first and second derivatives of the selfenergy. This bound is also a step in the program of rigorous (non-perturbative) study of the BCS phase transition for many Fermions systems; it proves in particular that in dimension two the transition temperature (if any) must be non-perturbative in the coupling constant. The proof is organized into two parts: the present paper deals with the convergent contributions, and a companion paper (Part II) deals with the renormalization of dangerous two point subgraphs and achieves the proof.