Beyond universality in repulsive SU(N) Fermi gases

TL;DR

This paper extends perturbation theory to third order for SU(N) Fermi gases, revealing how spin and interaction potential influence ferromagnetic phase transitions, with implications for ultracold atomic experiments.

Contribution

It generalizes perturbation theory for SU(N) fermions up to third order and analyzes phase transition nature across different spins and potentials.

Findings

Phase transition guaranteed for hard-sphere potential.

Higher spins lead to lower critical densities.

Multiple transition types observed depending on spin and potential.

Abstract

Itinerant ferromagnetism in dilute Fermi gases is predicted to emerge at values of the gas parameter where second-order perturbation theory is not accurate enough to properly describe the system. We have revisited perturbation theory for SU(N) fermions and derived its generalization up to third order both in terms of the gas parameter and the polarization. Our results agree satisfactorily with quantum Monte Carlo results for hard-sphere and soft-sphere potentials for $S = 1/2$. Although the nature of the phase transition depends on the interaction potential, we find that for a hard-sphere potential a phase transition is guaranteed to occur. While for $S= 1/2$ we observe a quasi-continuous transition, for spins $3/2$ and $5/2$, a first-order phase transition is found. For larger spins, a double transition (combination of continuous and discontinuous) occurs. The critical density reduces drastically when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin $5/2$ and $9/2$, respectively, are reported.