Effect of single-ion anisotropy on S=1 Heisenberg antiferromagnetic chain in Schwinger boson mean-field theory

We use the Schwinger boson mean-field theory, in which the constraint is imposed on the average, to the quantum Heisenberg antiferromagnetic chain with single-ion anisotropy (D > 0). Under the mean-field approximation to decouple the biquadratic term by introducing two HS fields and take the short range correlation and the coupling of on-site bosons into account, we find a clear and direct description for this system, and get two excitation spectra at T = 0 K, which distinguish the s(z) = 0 singlet and s(z) = +/-1 doublet. We also see that the relative phase of the two HS fields, having the lowest energy is the one equal to zero.