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We explore the zero-temperature phase diagram of a one-dimensional gascomposed of three-color fermions, which interact locally and with their nextneighbors. Using the density matrix renormalization group method andconsidering one-third filling, we characterize the ground state for severalvalues of the parameters, finding diverse phases, namely: phase separation,spin density wave, pairing phase, a metallic phase, two differentcharge-density waves, and a non-separable state with modulation of charge. Weshow that the von Neumann block entropy and the fidelity susceptibility areuseful for estimating the borders between the phases.

Phase diagram of the SU$(3)$ Fermi-Hubbard model with next-neighbor interactions