On the Problem of Spin Diffusion in 1D Antiferromagnets

We study the problem of spin diffusion in magnetic systems without long-range order. We discuss the example of the 1D spin chain. For the system described by the Heisenberg Hamiltonian we show that there are no diffusive excitations. However, the addition of an arbitrarily small dissipation term, such as the spin-phonon interaction leads to diffusive excitations in the long time limit. For those excitations we estimate the spin-diffusion coefficient by means of the renormalisation group analysis.