Flux quantization and pairing in one-dimensional copper-oxide models

We obtain the ground-state energy ${\mathit{E}}_0$(Φ) exactly as a function of flux Φ in a one-dimensional ‘‘copper-oxide model’’ on rings of finite circumference L, including on-site interactions and a nearest-neighbor interaction V. For V of the order of the charge-transfer gap or larger, the model extrapolated to large L exhibits flux quantization with charge 2e, and a slow algebraic decay of the singlet superconducting correlation function on oxygen sites. The extrapolated superfluid stiffness appears, however, finite only for not too large V. These results suggest a superconductive state at V of order the charge-transfer gap of the model, but a paired and phase-separated state at larger V.