Propagating S=1/2 particles in S=1 Haldane-gap systems

Inspired by the recent experiments on ${\mathrm{Y}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Ca}}_{\mathit{x}}$${\mathrm{BaNiO}}_5$, we discuss the dispersion relation of the S=1/2 particles in the S=1 Heisenberg and valence bond solid model in the limit of small hopping amplitudes. The effective S=1/2 edge spins mix with the spin of the impurity resulting in one fourfold and two twofold degenerate bands. We briefly discuss the interaction between the S=1/2 particles arising from the background.