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 ∝x^-γ of the charge-density and ∝x^-1/γ of the superconducting pairing correlation functions. To leading order in the doping δ away from half filling and t_⊥/t, we find γ=1 +(ρ²/8)(t_⊥/t)²δ² (t and t_⊥ 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.