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 $1/k^α$, where $k$ is the wave-vector of the modulations on the random coupling landscape. By using 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 $α> 1$, the wave-packet mean-square displacement changes from a long-time super-diffusive behavior for $α<1$ to a long-time ballistic behavior for $α> 1$. At the vicinity of $α=1$, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as $E_c\propto (α-1)^{1/3}$.