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

Abstract

Using a new impurity density matrix renormalization group scheme, we establish a reliable picture of how the low lying energy levels of a $S=1$ Heisenberg antiferromagnetic chain change {\it quantitatively} upon bond doping. A new impurity state gradually occurs in the Haldane gap as $J&#39; < J$, while it appears only if $J&#39;/J>γ_c$ with $1/γ_c=0.708$ as $J&#39;>J$. The system is non-perturbative as $1\leq J&#39;/J\leqγ_c$. This explains the appearance of a new state in the Haldane gap in a recent experiment on Y$_{2-x}$Ca$_x$BaNiO$_5$ [J.F. DiTusa, et al., Phys. Rev. Lett. 73 1857(1994)].