  We study the one-dimensional extended Hubbard model with alternating size of
the hopping integrals using the density-matrix renormalization group method. We
calculate the spin gap, the Tomonaga-Luttinger parameter, and the
charge-density-wave order parameter for various dimerizations, interaction
strengths, and band fillings. At half band-filling the spin and charge
excitations are gapped but these gaps disappear for infinitesimal hole doping.
At quarter filling, the Umklapp scattering in the half-filled lower Peierls
band generates a gap for the charge excitations but the gapless spin
excitations can be described in terms of an effective antiferromagnetic
Heisenberg model. Beyond a critical strength for the nearest-neighbor
interaction, the dimerized extended Hubbard model at quarter filling develops a
charge-density-wave ground state. The dimerization and the nearest-neighbor
Coulomb interaction strongly reduce the Tomonaga-Luttinger parameter from its
value for the bare Hubbard model. We discuss the relevance of our findings for
the Bechgaard salts.
