A Two Dimensional Fermi Liquid. Part 1: Overview

TL;DR

This paper proves the convergence of perturbation expansions for a class of two-dimensional interacting fermion models with asymmetric Fermi surfaces, establishing the existence of a Fermi liquid with a discontinuity in particle density.

Contribution

It provides a rigorous proof of convergence for zero-temperature perturbation series in 2D Fermi liquids with asymmetric Fermi surfaces, a significant step in many-fermion theory.

Findings

Convergence of perturbation expansions established

Existence of a discontinuity in particle density confirmed

Framework applicable to models with short-range interactions

Abstract

In a series of ten papers, of which this is the first, we prove that the temperature zero renormalized perturbation expansions of a class of interacting many-fermion models in two space dimensions have nonzero radius of convergence. The models have "asymmetric" Fermi surfaces and short range interactions. One consequence of the convergence of the perturbation expansions is the existence of a discontinuity in the particle number density at the Fermi surface. Here, we present a self contained formulation of our main results and give an overview of the methods used to prove them.