Numerical-Diagonalization Analyses of an Effective Hamiltonian for the Haldane System

Numerical-diagonalization analyses of an effective Hamiltonian for the Haldane system are given; the phase diadram of this Hamiltonian was previously studied only by means of the Hatree-Fock approximation. Phase transitions of the transverse-Ising-model type are found, and the phase diagram in the λ- D plane is depicted. The dependence of the phase boundary on the next-nearest-neighbor competing interaction is also studied in this effective-Hamiltonian formalism. A physical point of view is obtained by inspecting the low-lying excitation spectra of the effective Hamiltonian, and the correspondence to the original Haldane system is discussed.