Slater and Mott insulating states in the SU(6) Hubbard model

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 $\eta_{\rm VBS}=0.98\pm 0.01$.