  We present results for the spin conductance of the one dimensional spin-1/2
Heisenberg and XY model coupled to phonons. We apply an approach based on the
Stochastic Series Expansion (Quantum Monte Carlo) method to evaluate the
conductance for a variety of phonon dispersions and values of spin-phonon
coupling. From our numerical simulations and analytical arguments, we derive
several scaling laws for the conductance.
