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

We study the effect of the spin-phonon coupling on spin transport in the S = 1 one-dimensional Heisenberg antiferromagnet. The spin conductivity is calculated using the modified spin wave theory and the Kubo formalism of transport. We calculate the regular part of the spin conductivity, σ ^reg (ω), as function of the frequency at finite temperature. We obtain a strong effect of the magnon-phonon interaction on magnon transport.