  We perform a variational Gutzwiller calculation to study the ground state of
the repulsive SU(3) Hubbard model on the Bethe lattice with infinite
coordination number. We construct a ground-state phase diagram focusing on
phases with a two-sublattice structure and find five relevant phases: (1) a
paramagnet, (2) a completely polarized ferromagnet, (3) a two-component
antiferromagnet where the third component is depleted, (4) a two-component
antiferromagnet with a metallic third component (an "orbital selective" Mott
insulator), and (5) a density-wave state where two components occupy dominantly
one sublattice and the last component the other one. First-order transitions
between these phases lead to phase separation. A comparison of the SU(3)
Hubbard model to the better-known SU(2) model shows that the effects of doping
are completely different in the two cases.
