Multifractality of one electron eigen states in 1D disordered long range models

Abstract

One investigates the spatial structure of one-electron eigenstates for the one-dimensional Anderson model with long-range off-diagonal disorder h n,m=[−1, +1]/|n−m| δ where [a, b] means a uniform random distribution between a and b. Two cases are considered according to the choices for the on-site energy ε n , namely, ε n =0 and ε n=[0, 1] . For δ=1 all states are critical and the multifractal spectra f (α) is computed for the states near the center of the band. The level-spacing distribution function is also obtained and its behavior for both small and large separations are studied.