Effect of the hole doping into the Haldane-gap state on the one-dimensional S = 1 t-J model

The ground state and the excitation spectra of the S = 1 Heisenberg spin chain with hole hopping are investigated by means of the numerical-diagonalization method and with the help of the Zhang-Arovas picture. The phase diagrams for both the spin and charge sectors are sketched. As for the charge sector, two phases are found: Namely, a phase separation occurs in the weak-hopping region, while the system shows a Tomonaga-Luttinger-liquid phase in the strong-hopping region. In spite of the presence of the spin gap, the present phase diagram is similar to that reported for the S = 1/2 t-J chain with gapless spin excitations rather than to that for the magnetically frustrated t-J chain with a spin gap. In the spin sector, the string correlation is found to persist even in the over-doped area except in a region, which can be characterized by non-zero value of a generalized string correlation.