Bond-versus-site doping models for off-chain-doped Haldane-gap system Y${}_2$ Ba Ni O${}_5$

Using the density matrix renormalization-group technique, we calculate the impurity energy levels for two different effective models of off-chain doping for quasi-one-dimensional Heisenberg chain compound Y${}_2$ Ba Ni O${}_5$: ferromagnetic bond doping and antiferromagnetic site spin-1/2 doping. Thresholds of the impurity strength for the appearance of localized states are found for both models. However, the ground-state and low-energy excitations for weak impurity strength are different for these two models and the difference can be detected by experiments.