Impurity state in the Haldane gap for anS=1Heisenberg antiferromagnetic chain with bond doping

Using an impurity density-matrix renormalization-group scheme, we establish a reliable picture of how the low-lying energy levels of an $S=1\mathrm{}$ Heisenberg antiferromagnetic chain change quantitatively upon bond doping. An impurity state gradually occurs in the Haldane gap as $J^{\prime }<J$, while it appears only if $\frac{J^{\prime }}{J}>{\gamma }_c$ with $\frac{1}{{\gamma }_c}=0.708\mathrm{}$ as $J^{\prime }>J$. The spin polarization in the impurity state shows a localization-delocalization transition at ${\gamma }_c$. The system is nonperturbative as $1<~\frac{J^{\prime }}{J}<~{\gamma }_c$. It can explain the appearance of a new state in the Haldane gap recently observed experimentally on ${\mathrm{Y}}_{2-x}{\mathrm{Ca}}_x\mathrm{BaNi}{\mathrm{O}}_5$ [J.F. DiTusa et al., Phys. Rev. Lett. 73, 1857 (1994)].