Theory of two-spin infrared absorption in one-dimensional antiferromagnets: Improved Green's function theory and classical moments

We describe an improved treatment of an earlier Green's-function theory of the two-spin infrared absorption in a one-dimensional antiferromagnetic paramagnet and compare it with two exact classical moments of the same response function and the three-pole approximation using these moments. In particular, we remove a truncation approximation used in the original theory and confirm the conjecture made in the earlier work that the spectrum would peak at twice the two-spin-wave zone-boundary frequency at low temperatures. The Green's-function and classical theories agree quite well at low temperatures but differ markedly for temperatures TTMF1 when TMF is the mean-field transition temperature. We argue that the three-pole approximation is the more reliable of the two approaches at high temperatures.