  We perform large scale projector determinant quantum Monte-Carlo simulations
to study the insulating states of the half-filled SU(6) Hubbard model on the
square lattice. The transition from the antiferromagnetic state to the valence
bond solid state occurs as increasing the Hubbard $U$. In contrast, in the
SU(2) and SU(4) cases antiferromagnetism persists throughout the entire
interaction range. In the SU(6) case, antiferromagnetism starts to develop in
the weak interacting regime based on the Slater mechanism of Fermi surface
nesting. As $U$ passes a crossover value $U^*/t\approx 9$, the single-particle
gap scales linearly with $U$, marking the onset of Mott physics. In the Mott
regime, antiferromagnetism becomes to be suppressed as $U$ increases, and
vanishes after $U$ passes the critical value $U_{\rm AF,c}/t=13.3\pm 0.05$. The
critical exponents are obtained via critical scalings as $\nu_{\rm AF}=0.60\pm
0.02$ and $\eta_{\rm AF}=0.44\pm 0.03$. As $U$ further increases, the valence
bond solid ordering appears exhibiting the anomalous dimension $\eta_{\rm
VBS}=0.98\pm 0.01$.
