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We employ the determinant projector quantum Monte-Carlo method to investigatethe ground state magnetic properties in the Mott insulating states of thehalf-filled SU(4) and SU(6) Fermi-Hubbard model in the 2D square lattice, whichis free of the sign problem. The long-range antiferromagnetic Neel order isfound for the SU(4) case with a small residual Neel moment. Quantumfluctuations are even stronger in the SU(6) case. Numeric results areconsistent with either a vanishing or even weaker Neel ordering than that ofSU(4).

Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: a quantum Monte Carlo study