Energy Versus Magnetic-Field Diagram of the Spin-1 Haldane System with an Impurity

Energy versus magnetic-field diagram of the spin-$1$ Haldane system with an impurity bond is studied in terms of spin-1/2 degree of freedom at the sites neighboring the impurity bond by means of analytical method. We examine the equivalence between the realistic Hamiltonian and the phenomenological Hamiltonian which is composed two spin-1/2 spins representing the spin-1/2 degree of freedom. It is proved that when the strength of the impurity bond is sufficiently weak, the two Hamiltonians are equivalent to each other, as far as the energies of the low-lying states are concerned. We determine the correspondence between the interaction constants in the phenomenological Hamiltonian and those in the realistic Hamiltonian.