Artificial SU(3) spin-orbit coupling and exotic Mott insulators

Motivated by recent progress in the realization of artificial gauge fields and SU(N) Mott insulators using alkaline-earth-like atoms in optical lattices, we develop an unbiased SU(N) real-space dynamical mean-field theory approach to study the effect of spin-orbit coupling and on-site Hubbard interaction U on SU(3) fermionic systems. We investigate the behavior of the local magnetization, double occupancies, and the triple occupancy versus the Hubbard interaction across the metal to Mott insulator transition. We map out the magnetic phase diagram in the large-U limit and show that the spin-orbit coupling can stabilize long-range orders such as ferromagnets, spirals, and stripes with different orientations in SU(3) Mott insulators.