Spinons, solitons, and magnons in one-dimensional Heisenberg-Ising antiferromagnets

We calculate the excitation spectra for the 1D Heisenberg-Ising antiferromagnets by expansions around the Ising limit. For S = 1/2, the calculated expansion coefficients for the spinon spectra agree term by term with the solution of Johnson and McCoy. For S = 1, the solitons become gapless before the Heisenberg limit is reached, signaling a transition to the Haldane phase. By applying a staggered field we calculate the one-magnon spectra for the S = 1 Heisenberg chain. For S = 3/2 the quantum renormalization of the spin-wave spectra is calculated to be approximately 1.16.