Coulomb Correlations and Instability of Spinless Fermion Gas in 1D and 2D

TL;DR

This paper investigates the stability of spinless fermion gases in one and two dimensions, revealing that the Fermi liquid phase is inherently unstable in 1D and only conditionally stable in 2D based on density and interaction strength.

Contribution

It provides a detailed phase diagram showing the conditions under which the Fermi liquid phase remains stable or becomes unstable in 1D and 2D systems.

Findings

Fermi liquid phase is never stable in 1D.

Fermi liquid phase has limited stability in 2D.

Stability depends on density and interaction strength.

Abstract

We study the stability of the ordinary Landau Fermi liquid phase for interacting, spinless electrons. We require causality and demand that the Pauli principle be obeyed. We find a phase diagram determined by two parameters: the particle density and the interaction strength. We find that the homogeneous, constant density Fermi liquid phase of a spinless Fermion gas is {\em never} stable in 1D, but that it may have a restricted domain of stability in 2D.