Effects of the single-ion anisotropy and dimerization on 1D spin-1 antiferromagnetic Heisenberg chain

Abstract

One-dimensional quantum spin-1 antiferromagnetic Heisenberg chain (AFHC) with exchange anisotropy J z , dimerization δ and single-ion anisotropy D∑ n ( S n z ) 2 was investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the excitation spectrum, phase order and the phase fluctuation φ were derived in a self-consistent-harmonic-field approach. We studied the effects of the single-ion anisotropy and dimerization on two gaps by taking the different momentum cutoff α i in two scalar field spaces H i ( i=1,2). The occurrences of richer phase transitions were understood in the viewpoints of the phase fluctuation and the z polar spin fluctuation. And the Gaussian critical line was given as J z − D− πα 1 δ=0.