Extended spin waves in aperiodic ferromagnetic chains

In this work, a one-dimensional quantum Heisenberg ferromagnet with aperiodic exchange couplings is considered. To produce an aperiodic distribution of exchange couplings, it is used a sinusoidal function whose phase φ varies as a power-law, φ∝n^ν, where n labels the positions along the chain. By using exact diagonalization, the spin-wave participation number and the local density of states are computed. The numerical calculations indicate that for 0 < ν < 1, this ferromagnetic system displays a phase of extended spin waves in the low-energy region. For ν > 1 all spin waves are localized except for the zero energy mode. By integrating the time-dependent Schr?dinger equation, the temporal evolution of the mean-square displacement of the wave-packet was followed. Associated with the emergence of extended spin waves, it was observed that the wave-packet mean-square displacement displays a ballistic spread.