Impurity Energy Level Within The Haldane Gap

Abstract

An impurity bond $J{&#39;}$ in a periodic 1D 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 $J{&#39;}<J$ the level changes gradually from the edge of the Haldane gap to the ground state energy as the deviation $dev=(J-J{&#39;})/J$ changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when $J{&#39;}>J$. The impurity level appears only when the deviation $dev=(J{&#39;}-J)/J{&#39;}$ is greater than $B_{c}$, which is near 0.3 in our calculation.