Finite-size scaling of power-law bond-disordered Anderson models

We investigate numerically the nature of energy eigenstates in one-dimensional bond-disordered Anderson models with hopping amplitudes decreasing as H(ij)proportional to1/\i-j\(alpha). The eigenstates become delocalized whenever the hopping amplitudes decay slower than 1/r. By performing an exact diagonalization scheme on finite chains, we compute the participation ratio of all energy eigenstates. Employing a finite-size scaling analysis, we report on the relevant scaling exponents characterizing this delocalization transition as well as the level-spacing distribution at the critical point alpha=1. The random hopping amplitudes are taken from both uniform and random sign distributions. We show that these models display similar critical behavior in the vicinity of alpha=1. However, the random sign model exhibits an asymptotic delocalization in the limit of alpha-->infinity and the universal scaling behavior in this regime is also reported.