Phase Separation and Superconductivity in the Copper Oxide Chain

The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V, is determined. Phase separation takes place above a critical value of $V$ when the Cu2+ to Cu+ valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger Liquid theory applies and calculate the contours of the charge-charge correlation exponent K_{\rho}. We show that anomalous flux quantization occurs as$K_{\rho} diverges. At n = 1, for V > t, a gap opens in the spectrum and the ground state is a charge-density wave.