Mean-field study of itinerant ferromagnetism in trapped ultracold Fermi gases: Beyond the local density approximation

TL;DR

This paper presents a mean-field theoretical analysis of itinerant ferromagnetism in trapped ultracold Fermi gases, highlighting the limitations of the local density approximation and identifying the phase transition through free energy shape changes.

Contribution

It introduces a self-consistent Hartree-Fock approach beyond the local density approximation to accurately study ferromagnetic transitions in trapped ultracold Fermi gases.

Findings

LDA is valid in the paramagnetic phase but not after the ferromagnetic transition.

The phase transition is identified by changes in the free energy curve with polarization.

Quantitative discrepancies arise in thermodynamic quantities when using LDA post-transition.

Abstract

We theoretically investigate the itinerant ferromagnetic transition of a spherically trapped ultracold Fermi gas with spin imbalance under strongly repulsive interatomic interactions. Our study is based on a self-consistent solution of the Hartree-Fock mean-field equations beyond the widely used local density approximation. We demonstrate that, while the local density approximation holds in the paramagnetic phase, after the ferromagnetic transition it leads to a quantitative discrepancy in various thermodynamic quantities even with large atom numbers. We determine the position of the phase transition by monitoring the shape change of the free energy curve with increasing the polarization at various interaction strengths.