Antiferromagnetism of Repulsively Interacting Fermions in a Harmonic Trap

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 a system with balanced spin-mixtures on a square lattice, antiferromagnetism either appears in a checkerboard pattern or forms a ring, and the 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 the antiferromagnetic order is suppressed there.