Low temperature transport in the XXZ model

We present evidence suggesting that spin transport in the gapless phase of the S=1/2 XXZ model is ballistic rather than diffusive. We map the model onto a spinless fermion model whose charge stiffness determines the spin transport of the original model. By means of exact numerical diagonalisation and finite size scaling we study both the stiffness and the level statistics. We show that the stiffness is non-zero at low temperatures so that the transport is ballistic. Our results suggest that the non-zero stiffness is due to the fact that even in the presence of Umklapp scattering a non-zero fraction of states remain degenerate in the thermodynamic limit.