Dynamics of the quantum integer spin S one-dimensional Heisenberg antiferromagnet coupled to phonons

We present the low-temperature dynamic properties of the quantum one-dimensional Heisenberg antiferromagnet with integer spin S coupled to phonons. The calculation of the relaxation function is performed using the combination of the memory function formalism with the modified spin-wave theory. The procedure includes up to two-magnon and magnon-phonon processes. We show that the phonon-magnon coupling smooths the double-peak structure obtained for the model in the absence of phonons, when the wavevector q moves from q = pi.