Magnon delocalization in ferromagnetic chains with long-range correlated disorder

We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies $E$. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\propto 1\mathrm{/}{k}^{\alpha }$. We found that for $\alpha <1$, one-magnon excitations remain exponentially localized with the localization length $\xi$ diverging as 1/E. For $\alpha =1$ a faster divergence of $\xi$ is obtained. For any $\alpha >1$, a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.