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We apply Dynamical Mean-Field Theory to strongly interacting fermions in aninhomogeneous environment. With the help of this Real-Space DynamicalMean-Field Theory (R-DMFT) we investigate antiferromagnetic states ofrepulsively interacting fermions with spin 1/2 in a harmonic potential. WithinR-DMFT, antiferromagnetic order is found to be stable in spatial regions withtotal particle density close to one, but persists also in parts of the systemwhere the local density significantly deviates from half filling. In systemswith spin imbalance, we find that antiferromagnetism is gradually suppressedand phase separation emerges beyond a critical value of the spin imbalance.

Antiferromagnetic Order of Strongly Interacting Fermions in a Trap: Real-Space Dynamical Mean-Field Analysis