One-magnon excitations in Heisenberg ferromagnetic chains with power-law decaying random interactions

We investigate the nature of one-magnon excitations in disordered quantum Heisenberg ferromagnetic chains with long-range interactions. The exchange coupling between a given pair of sites (i,j) is considered to be randomly distributed with asymptotic power-law decaying variance ΔJ∝1/|i−j|α. By employing an exact diagonalization procedure on finite chains, we compute the density of states, the localization length and associated fluctuations of all one-magnon eigenstates within the band of allowed energies E. We observe that for α>2 the behavior is the same one typical of disordered ferromagnetic chains with short-range interactions with all eigenstates with finite energy being exponentially localized. Delocalized one-magnon states of finite energy emerges for slowly decaying interactions.