Magnetism and domain formation in SU(3)-symmetric multi-species Fermi mixtures

We study the phase diagram of an SU(3)-symmetric mixture of three-component ultracold fermions with attractive interactions in an optical lattice, including the additional effect on the mixture of an effective three-body constraint induced by three-body losses. We address the properties of the system in D >= 2 by using dynamical mean-field theory and variational Monte Carlo techniques. The phase diagram of the model shows a strong interplay between magnetism and superfluidity. In the absence of the three-body constraint (no losses), the system undergoes a phase transition from a color superfluid (c-SF) phase to a trionic phase, which shows additional particle density modulations at half-filling. Away from the particle-hole symmetric point the c-SF phase is always spontaneously magnetized, leading to the formation of different c-SF domains in systems where the total number of particles of each species is conserved. This can be seen as the SU(3) symmetric realization of a more general tendency for phase separation in three-component Fermi mixtures. The three-body constraint strongly disfavors the trionic phase, stabilizing a (fully magnetized) c-SF also at strong coupling. With increasing temperature we observe a transition to a non-magnetized SU(3) Fermi liquid phase.