Failure of Fermi Liquid Theory in 2-D: A Signal from Perturbation Theory

TL;DR

This paper investigates the limitations of Fermi liquid theory in two dimensions by analyzing perturbative corrections, revealing an induced long-range interaction that suggests potential instability of the Fermi liquid ground state.

Contribution

It demonstrates that perturbation theory indicates a long-range repulsive interaction in 2D Fermi gases, challenging the stability of the Fermi liquid ground state.

Findings

Induced long-range ${1/r^2}$ interaction among electrons

Potential instability of the 2D Fermi liquid ground state

Perturbation theory reveals limitations of Fermi liquid theory in 2D

Abstract

We study the perturbative correction to the ground state energy eigenvalue of a 2-dimensional dilute fermi gas with weak short-range two body repulsion. From the structure of the energy shift we infer the presence of an induced two body long range repulsive interaction $ {\displaystyle {1\over{r^2}} }$ among the constituent electrons indicating a potential instability of the fermi liquid ground state.