  In optical lattices attractive ultracold fermions with three hyperfine-spin
components (colors) can form three fermionic configurations depending on
interactions: unbound fermion, on-site trion and off-site trion, leading to the
coexistence of multiple Fermi species in the ordered phase, which manifests
that the attractive three-color fermions are unique from other correlated
fermion systems and may host intriguing phases and phase transitions. At
temperature below the superexchange energy scale, we employ the determinant
quantum Monte Carlo (QMC) method to investigate the phases and phase
transitions in the half-filled attractive three-color Hubbard model on a
honeycomb lattice where Hubbard interactions are color-dependent (anisotropic
interactions) and the coupling between color 3 and colors (1, 2) serves as a
control parameter. In the coupling regime where on-site and off-site trions
coexist, our QMC simulations demonstrate coexisting N\'eel and charge density
wave orders which are common in condensed matter but rare in ultracold atoms.
At weak coupling where the color superfluid (CSF) order is scattered by color-3
fermions, we find that very small coupling of color 3 with colors (1, 2) can
destroy the CSF order and the vanishing of the CSF order is not immediately
accompanied by the emergence of the on-site trionic phase, which strikingly
disagrees with the prevalent results of dynamical mean-field theory. The
underlying mechanisms of the coexisting charge/spin orders and the CSF order
breaking are also presented based on intuitive physical pictures.
