Exchange interactions in the Hubbard-Stratonovich transformation for the stability analysis of itinerant ferromagnetism

TL;DR

This paper introduces a new method to incorporate exchange interactions explicitly in the analysis of itinerant ferromagnetism in ultracold Fermi gases, revealing stability restrictions in the phase diagram due to strong interactions.

Contribution

It develops a modified interaction potential that explicitly includes exchange effects within the path-integral formalism for analyzing itinerant ferromagnetism.

Findings

Exchange interactions are lost in the Hubbard-Stratonovich transformation.

Explicit inclusion of exchange effects restricts the ferromagnetic phase.

Strong interactions lead to instability against density fluctuations.

Abstract

Itinerant ferromagnetism, i.e. spontaneous polarization of non-localized particles, is expected to occur for strong repulsive interactions in a spin-1/2 Fermi system. However, this state has proven notoriously hard to find experimentally, both in ultracold gases and in solids. This raises questions about the stability of the itinerant ferromagnetic state itself. Here we develop a new approach to describe both the direct and exchange interactions for a general interaction potential in the path-integral formalism and we apply this method to itinerant ferromagnetism in three-dimensional ultracold Fermi gases. We show that the exchange interactions are lost in the Hubbard-Stratonovich transformation and we propose to explicitly include the exchange effects in a new modified interaction potential. In the saddle-point approximation, the effect of interactions can be taken into account using only three parameters. If the interactions become too strong, all saddle points become unstable to density fluctuations. This greatly restricts the area in the phase diagram where uniform itinerant ferromagnetism is expected to occur.