Anomalous behavior of the charge and spin degrees of freedom in the CuO double chains of PrBa2Cu4O8

The density-matrix renormalization-group method is used to study the electronic states of a two-chain Hubbard model for CuO double chains of PrBa2Cu4O8. We show that the model at quarter filling has charge-ordered phases with stripe-type and in-line-type patterns in the parameter space, and in between, there appears a wide region of vanishing charge gap; the latter phase is characteristic of either a Tomonaga-Luttinger liquid or a metallic state with a spin gap. We argue that the low-energy electronic state of the CuO double chains of PrBa2Cu4O8 should be in the metallic state with a possibly small spin gap.