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

One investigates the spatial structure of one-electron eigenstates for the one-dimensional Anderson model with long-range off-diagonal disorder hn,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 εn, namely, εn=0 and εn=[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.