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 $S(k)\ensuremath{\propto}{1/k}^{\ensuremath{\alpha}}.$ We found that for $\ensuremath{\alpha}<1,$ one-magnon excitations remain exponentially localized with the localization length $\ensuremath{\xi}$ diverging as
1/E. For $\ensuremath{\alpha}=1$ a faster divergence of $\ensuremath{\xi}$ is obtained. For any $\ensuremath{\alpha}>1,$ 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.
We study the nature of collective two-spin excitations in disordered
S=1∕2 ferromagnetic chains. Using a direct diagonalization scheme, we characterize the two-magnon eigenstates by computing their spacial extent, two-point correlation and the average distance between the excited spins within the allowed energy band. We found that, due to the effective excitation interaction imposed by the exclusion rule, the low-energy two-magnon states display strong spin-spin correlations as compared to the more localized high-energy states. We further solve the time-dependent Schroedinger equation to follow the time evolution of an initially localized two-magnon state. We show that the effective one-magnon wave packet develops power-law tails with distinct exponents for the left and right tails, with the distribution function of the spin-spin distance decaying as $P(d)\ensuremath{\propto}1∕d$. We show that the average distance between the two excited spins evolves in time diffusively, while the wave-packet dispersion evolves superdiffusively.
We calculate the ground-state two-spin correlation functions of spin-
21 quantum Heisenberg chains with random exchange couplings using the real-space renormalization-group scheme. We extend the conventional scheme to take account of the contribution of local higher multiplet excitations in each decimation step. This extended scheme can provide highly accurate numerical data for large systems. The random average of staggered spin correlations of the chains with random antiferromagnetic (AF) couplings shows algebraic decay like
1/r2, which verifies the Fisher's analytic results. For chains with random ferromagnetic (FM) and AF couplings, the random average of generalized staggered correlations is found to decay more slowly than a power law, in the form close to
1/ln(r). The difference between the distribution functions of the spin correlations of the random AF chains and of the random FM-AF chains is also discussed.