Antiferromagnetism of Repulsively Interacting Fermions in a harmonic trap

TL;DR

This paper introduces a Real-Space Gutzwiller variational method to study antiferromagnetism in ultracold fermions with repulsive interactions in a harmonic trap, revealing stable antiferromagnetic regions near unit density and suppression in imbalanced cases.

Contribution

It develops and applies a novel Real-Space Gutzwiller approach to analyze antiferromagnetism in trapped ultracold fermions, aligning with and extending previous theoretical results.

Findings

Antiferromagnetism forms checkerboard or ring patterns.

Antiferromagnetic order is stable near particle density of one.

Order is suppressed in imbalanced spin cases.

Abstract

We propose a Real-Space Gutzwiller variational approach and apply it to a system of repulsively interacting ultracold fermions with spin 1/2 trapped in an optical lattice with a harmonic confinement. Using the Real-Space Gutzwiller variational approach, we find that in system with balanced spin-mixtures on a square lattice, antiferromagnetism either appears in a checkerboard pattern or forms a ring and antiferromagnetic order is stable in the regions where the particle density is close to one, which is consistent with the recent results obtained by the Real-Space Dynamical Mean-field Theory approach. We also investigate the imbalanced case and find that antiferromagnetic order is suppressed there.