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

TL;DR

This study investigates how long-range correlated disorder affects spin-wave localization and dynamics in a one-dimensional quantum Heisenberg ferromagnet, revealing a transition from super-diffusive to ballistic behavior at a critical correlation threshold.

Contribution

It demonstrates the emergence of extended spin-waves and a mobility edge in a disordered ferromagnetic chain with power-law correlated exchange couplings, using multiple analytical and numerical methods.

Findings

Extended spin-waves appear for ter than 1

Wave-packet dynamics shift from super-diffusive to ballistic at ter 1

Mobility edge scales as ( - 1)^{1/3} near the transition

Abstract

We study the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, 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 $\alpha > 1$, the wave-packet mean-square displacement changes from a long-time super-diffusive behavior for $\alpha <1$ to a long-time ballistic behavior for $\alpha > 1$. At the vicinity of $\alpha =1$, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as $E_c\propto (\alpha -1)^{1/3}$.