Contact potential instability in the path-integral description of itinerant ferromagnetism

TL;DR

This paper investigates the stability of itinerant ferromagnetism in a two-component Fermi gas using path-integral formalism, revealing that all extrema are unstable, which explains the experimental difficulty in observing the phase transition.

Contribution

It introduces a path-integral approach to analyze the stability of itinerant ferromagnetism, highlighting the importance of considering mechanical stability and realistic interactions.

Findings

All extrema of the action are unstable to density fluctuations.

Mechanical instability affects both polarized and normal states.

Contact potential may be insufficient; realistic potentials are recommended.

Abstract

It has long been predicted that a two-component non-localized Fermi gas will exhibit spontaneous polarization for sufficiently strong repulsive interactions, a phenomenon which is called itinerant ferromagnetism. Recent experiments with ultracold atomic gases have reached the interaction strength for which theoretical models have predicted the occurrence of the normal-to-itinerant-ferromagnetic phase transition, but so far this transition has not been observed. The instability of the repulsive branch of the Feshbach resonance prevents the formation of the itinerant ferromagnetic state, but it is not clear whether this is the only instability impeding its experimental realization. In this article, we use the path-integral formalism with density fields in the Hubbard-Stratonovich transformation to study the stability of a homogeneous two-component Fermi gas with contact interactions. Within the saddle-point approximation we show that none of the extrema of the action are minima, meaning all extrema are unstable to small density fluctuations. This implies a more general mechanical instability of the polarized (itinerant ferromagnetic) and normal states of the system in the path-integral formalism. We find that it is important to consider the stability of the system when studying itinerant ferromagnetism. Since (mechanical) stability may be influenced by the details of the interaction potential, we suggest the use of a more realistic potential than the contact potential in future theoretical descriptions.