Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange

Abstract

We study the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to ${1/k}^{\ensuremath{\alpha}},$ where k is the wave vector of the modulations on the random coupling landscape. By using the renormalization group, integration of the equations of motion, and exact diagonalization, we compute the spin-wave localization length and the mean-square displacement of the wave packet. We find that, associated with the emergence of extended spin waves in the low-energy region for \ensuremath{\alpha}>1, the wave-packet mean-square displacement changes from a long-time super diffusive behavior for \ensuremath{\alpha}1 to a long-time ballistic behavior for \ensuremath{\alpha}>1. At the vicinity of \ensuremath{\alpha}=1, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as ${E}_{c}\ensuremath{\propto}(\ensuremath{\alpha}\ensuremath{-}{1)}^{1/3}.$