Large N Thirring Matter in Three Dimensions

TL;DR

This paper analyzes a three-dimensional N-fermion system with Thirring interactions, demonstrating its consistency with Landau Fermi liquid theory and deriving exact correlation functions showing singular behavior at specific conditions.

Contribution

It provides an exact solution for the current-current correlation function in a 3D Thirring model at large N, linking it to Fermi liquid properties.

Findings

Model fits into Landau Fermi liquid theory

Exact current-current correlation function derived

Singular behavior at zero frequency and twice Fermi momentum

Abstract

In this paper we calculate properties of the three-dimensional system of N species of fermions at zero temperature and finite chemical potential, with the four-fermionic interaction of the Thirring type. We observe that this model fits consistently into framework of the Landau Fermi liquid theory, and possesses a non-trivial zeroth and first Landau parameters. Our result is derived to all orders of the Thirring coupling constant and to the leading order of the large-N expansion. In particular we solve for the exact current-current correlation function, and show that it exhibits a singular behavior at zero frequency and twice of the Fermi momentum.