Impurity Energy Level Within The Haldane Gap

Abstract

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

Latex file,9 pages uuencoded compressed postscript including 4 figures