Ground state of a mixture of SU(3) fermions and scalar bosons

We explore a system composed of scalar bosons and $\mathrm{SU}(3)$ fermions in one dimension. Considering only local intra- and interspecies interactions, the system is described by the Bose-Fermi-Hubbard Hamiltonian, which is studied using the density-matrix renormalization-group method. In addition to the common gapless and mixed-Mott-insulator phases, we identify unknown gapped states, in which bosons couple with some or all flavors of fermions. We unveil different flavor-selective states characterized by itinerant fermions that coexist with an insulator state in which the bosons connect with only one- or two-flavor fermions. The states reported here could be implemented in cold-atom experiments.