SUPER-DIFFUSION IN RANDOM CHAINS WITH CORRELATED DISORDER

We study the spin-wave dynamics of the one-dimensional Heisenberg ferromagnet with random exchange couplings J. The problem becomes equivalent to considering an electronic wavepacket put on an initial site in a chain with correlated off-diagonal disorder, where the bonds are random in pairs. The mean-square displacement of the wavepacket versus time is shown to display asymptotically super-diffusion (sigma-2(t) approximately t3/2) and localization (sigma-2(t) approximately const), depending on whether the average over the disorder [l/J] exists or not. In the critical intermediate case ordinary diffusion sigma-2(1) approximately t is obtained. We show that the dynamical behaviour relates closely to the corresponding spectral density and the localization length singularities whose type is demonstrated.