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