Mott transition and magnetism of SU(3) fermions in a square lattice

The SU(N) Fermi-Hubbard model is attracting strong ongoing interest for its connections to multi-orbital solid-state systems and its rich predicted phase diagrams. In this work we study the SU(3) Fermi-Hubbard model in the two-dimensional square lattice using determinant Quantum Monte Carlo (DQMC), as a function of the interaction strength U/t and temperature. Previous results in the strongly interacting limit, U/t >> 1, and one particle per site propose the existence of 2-sublattice ordering at high-T and 3-sublattice ordering at low-T. Here we explore if that also occurs at weak and moderate values of the interaction strength, and study the evolution of the compressibility and structure factors to understand at which interaction strengths the system opens a charge gap and when it develops magnetic ordering. These results provide guidance for ongoing optical lattice experiments with ¹⁷³Yb or ⁸⁷Sr quantum gas microscopes.