Fermi liquid behavior and Luttinger's theorem close to a diverging scattering length

TL;DR

This paper explores the thermodynamic behavior of a Fermi gas near a diverging scattering length, revealing a phase transition influenced by Luttinger's theorem and the effects of strong interactions on magnetic screening.

Contribution

It derives thermodynamic properties of a Fermi gas near a diverging scattering length, highlighting a phase transition and magnetic screening effects under strong interactions.

Findings

First order phase transition in the normal phase as a function of interaction strength.

Volume change at finite temperatures across the BEC-BCS crossover.

Screening of magnetic fields near the divergence of the scattering length.

Abstract

Based on the results obtained in a previous paper (S. Gaudio et al., cond-mat/0505309}, we derive the thermodynamic properties of a Fermi gas, deep into the quantum degenerate regime. We show that, if Luttinger's theorem holds, a first order phase transition occurs in the normal phase as a function of the interaction strength, U. We also show that a volume change occurs at finite temperatures from the BEC to the BCS side of a diverging s-wave scattering length, in the normal phase. The transition has an end point above the BCS critical temperature. Also we show that a paramagnetic system in equilibrium, close to the divergence of the scattering length, on the negative side, screens out any applied magnetic field.