Phases of the two-band model of spinless fermions in one dimension

We study the two-band model of spinless fermions in one dimension for weak repulsive interactions. In this case, the model is equivalent to the weakly interacting spinless two-leg ladder. We obtain nonuniversal analytic expressions for the power-law decays proportional to x(-gamma) of the charge-density and proportional to x(-1/gamma) of the superconducting pairing correlation functions. To leading order in the doping delta away from half filling and t(perpendicular to)/t, we find y=1 +(pi(2)/8)(t(perpendicular to)/t)(2)delta(2) (t and t(perpendicular to) are the hopping terms along and between the chains), such that superconducting pairing correlations dominate. We furthermore show that the transition from the superconducting phase to the usual one-dimensional (Luttinger) metal occurs via a mixed phase, where superconducting pairs are formed in the bonding band only. We give the phase diagram as a function of temperature and doping.