We consider a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and nearest-neighbor hopping for spin σ, which depends on the sum of particles ${\mathrm{m}}_{\mathrm{\sigma }-|\mathrm{A}\mathrm{m}}$ with opposite spin in the two sites involved. The hopping matrix elements are denoted by ${\mathrm{t}}_{\mathrm{AA}}$,${\mathrm{t}}_{\mathrm{AB}}$,${\mathrm{t}}_{\mathrm{BB}}$ for ${\mathrm{m}}_{\mathrm{\sigma }-|\mathrm{A}\mathrm{m}}$=0,1,2, respectively. For 0<${\mathrm{t}}_{\mathrm{AB}}$<${\mathrm{t}}_{\mathrm{AA}}$=${\mathrm{t}}_{\mathrm{BB}}$, we have determined the regions of parameters for which the ground-state (GS) of the one-dimensional system is a charge-density wave (CDW), a spin-density wave (SDW), or a metal (M), using Hartree-Fock, exact diagonalization of finite chains and quantum Monte Carlo. The results agree qualitatively with the exactly solvable limit of ${\mathrm{t}}_{\mathrm{AB}}$=0. For 0<${\mathrm{t}}_{\mathrm{AB}}$<${\mathrm{t}}_{\mathrm{AA}}$=${\mathrm{t}}_{\mathrm{BB}}$, the GS is a M for sufficiently low values of U and V. In contrast, when ${\mathrm{t}}_{\mathrm{AA}}$+${\mathrm{t}}_{\mathrm{BB}}$-${2\mathrm{t}}_{\mathrm{AB}}$=0, our results suggest that the GS is either a CDW or a SDW, with the boundary between them lying near the line U=2V.

DOI:https://doi.org/10.1103/PhysRevB.55.1173