Frustration and quantum fluctuation in spin-1 antiferromagnetic chains with competing interactions

Ground-state phase diagram and low-lying excitation spectrum of the one-dimensional S=1 anisotropic Heisenberg antiferromagnetic chain with nearest neighbor and next nearest neighbor interactions are studied by means of an approximate mapping of the original S=1 spin Hamiltonian to the effective fermion Hamiltonian, which describes the dynamics of spin zero defects in antiferromagnetic environments (domain walls in the Néel state). We find that the frustration due to the next nearest neighbor interactions works cooperatively with quantum fluctuation in the Haldane state and stabilizes it. This is naturally explained in terms of the spin zero defect. In addition, we discuss characteristic features of the excitation spectrum in connection with its ground-state properties.