Doping Induced Quantum Bound States within the Haldane Gap

Using the approach proposed by Zittartz and Müller-Hartmann [Z. Phys. 232, 11 (1970)], we show explicitly that quantum bound states at the centre of the Haldane energy gap can be induced by doping in a spin-1 linear chain Heisenberg antiferromagnet. We calculate the dynamic structure factor $S(q,\omega )$ due to these bound states and use it to interpret the recent neutron scattering experiments on doped ${\mathrm{Y}}_2{\mathrm{BaNiO}}_5$ [J. F. DiTusa et al., Phys. Rev. Lett. 73, 1857 (1994)].