Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model

We demonstrate a self-consistent variant of the constrained path quantum Monte Carlo approach and apply the method to compute ground state correlations in the SU(3) Fermi Hubbard Hamiltonian on a square lattice at 1/3-filling. We provide clear evidence of a quantum critical point(QCP) separating a non-magnetic uniform metallic phase from a regime where long-range 'spin' order is present. This discovery of multiple successive transitions to novel magnetic states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases, significantly extends previous work in the Heisenberg limit to itinerant fermions. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N) physics.