Interacting Fermi liquid in two dimensions at finite temperature: Part II: Renormalization

TL;DR

This paper rigorously proves that a two-dimensional interacting Fermi system at low temperature behaves as a Fermi liquid with controlled derivatives, establishing bounds on the selfenergy and implications for phase transition temperatures.

Contribution

It provides a rigorous proof that 2D Fermi liquids remain analytic in the coupling constant at low temperatures using renormalization group methods.

Findings

Fermi liquid behavior established at low T in 2D systems

Uniform bounds on derivatives of the selfenergy proven

Transition temperature must be non-perturbative in 2D

Abstract

This is a companion paper to cond-mat/9907130. Using the method of continuous renormalization group around the Fermi surface and the results of cond-mat/9907130, we achieve the proof 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./|log T| and satisfying uniform bounds on the first and second derivatives of the selfenergy. This proves that in two dimensions the transition temperature (if any) must be non-perturbative, and is a step in the program of rigorous study of the BCS phase transition using methods of constructive field theory.