Impurity energy level in the Haldane gap

An impurity bond ${\mathit{J}}^{\prime }$ in a periodic one-dimensional antiferromagnetic spin-1 chain with exchange J is considered. Using the numerical density matrix renormalization-group method, we find an impurity energy level in the Haldane gap, corresponding to a bound state near the impurity bond. When ${\mathit{J}}^{\prime }$<J the level changes gradually from the edge of the Haldane gap to the ground-state energy as the deviation dev=(J-${\mathit{J}}^{\prime }$)/J changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when ${\mathit{J}}^{\prime }$≳J. The impurity level appears only when the deviation dev=(${\mathit{J}}^{\prime }$-J)/${\mathit{J}}^{\prime }$ is greater than ${\mathit{B}}_{\mathit{c}}$, which is close to 0.3 in our calculation. © 1996 The American Physical Society.