  We explore the zero-temperature phase diagram of a one-dimensional gas
composed of three-color fermions, which interact locally and with their next
neighbors. Using the density matrix renormalization group method and
considering one-third filling, we characterize the ground state for several
values of the parameters, finding diverse phases, namely: phase separation,
spin density wave, pairing phase, a metallic phase, two different
charge-density waves, and a non-separable state with modulation of charge. We
show that the von Neumann block entropy and the fidelity susceptibility are
useful for estimating the borders between the phases.
