Impurity energy level in the Haldane gap

An impurity bond J' 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 J'<J the level changes gradually from the edge of the Haldane gap to the ground-state energy as the deviation dev=(J-J')/J changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when J'>J. The impurity level appears only when the deviation dev=(J'-J)/J' is greater than B-c, which is close to 0.3 in our calculation.