We study a Hubbard hamiltonian, including a quite general nearest-neighbor
interaction, parametrized by repulsion V, exchange interactions Jz, Jperp,
bond-charge interaction X and hopping of pairs W. The case of correlated
hopping, in which the hopping between nearest neighbors depends upon the
occupation of the two sites involved, is also described by the model for
sufficiently weak interactions. We study the model in one dimension with usual
continuum-limit field theory techniques, and determine the phase diagram. For
arbitrary filling, we find a very simple necessary condition for the existence
of dominant triplet superconducting correlations at large distance in the spin
SU(2) symmetric case: 4V+J<0. In the correlated hopping model, the three-body
interaction should be negative for positive V. We also compare the predictions
of this weak-coupling treatment with numerical exact results for the
correlated-hopping model obtained by diagonalizing small chains, and using
novel techniques to determine the opening of the spin gap.Comment: 8 pages, 3 figure