Critical wave-packet dynamics in the power-law bond disordered Anderson model

We investigate the wave-packet dynamics of the power-law bond disordered one-dimensional Anderson model with hopping amplitudes decreasing as H-nm proportional to vertical bar n-m vertical bar(-alpha). We consider the critical case (alpha=1). Using an exact diagonalization scheme on finite chains, we compute the participation moments of all stationary energy eigenstates as well as the spreading of an initially localized wave packet. The eigenstates multifractality is characterized by the set of fractal dimensions of the participation moments. The wave packet shows a diffusivelike spread developing a power-law tail and achieves a stationary nonuniform profile after reflecting at the chain boundaries. As a consequence, the time-dependent participation moments exhibit two distinct scaling regimes. We formulate a finite-size scaling hypothesis for the participation moments relating their scaling exponents to the ones governing the return probability and wave-function power-law decays.