Three-color fermions under local and next-neighbor interactions

Graphene, Bechgaard salts, polymers and systems of adatoms on semiconductor surfaces can be described by an extended SU(2) Fermi-Hubbard model, which has a rich phase diagram that has been studied for decades. Ultracold atom setups have allowed testing and extending many ideas and concepts of condensed matter. Confining alkaline-earth-metal atoms, which have several hyperfine states allow to obtain SU(N>2) Fermi-Hubbard systems experimentally.
We study three-color (N=3) fermions confined in a one-dimensional optical lattice and consider local and next-neighbor interactions, obtaining an extended SU(3) Fermi-Hubbard model. Using DMRG, we build a phase diagram that contains two different charge density wave phases, a phase separation and spin-density wave phases for a global density of one-third.