Multifractal structure of eigenstates in the Anderson model with long-range off-diagonal disorder

The spectrum of eigenvalues and the spatial structure of eigenstates for the Anderson model with long-range off-diagonal disorder (V-ij=(+/-)/\R-i-R-j\(d)) is investigated numerically where R-i are Poisson-distributed random points in d-dimensional space. For this marginal case all states in the system are delocalized. Analyzing the scaling with system size of the inverse participation numbers for the most extended modes we find that these states exhibit a self-similar multifractal structure. The generalized dimensions, D-q, and the multifractal spectrum, f(alpha), are calculated. For d=3 the information dimension D-1=2.65 and the correlation dimension D-2=2.33 that characterizes the power-law behavior of the averaged two-particle Green function. The temporal autocorrelation function C(t) built from the eigenstates of the most dispersive oscillator exhibits an nondiffusive algebraic decay C(t)similar to t(-delta) with the exponent delta=(D) over tilde D-2=D-2/d reflecting the generalized multifractal dimension of the local density of states. [S0163-1829(98)02617-4].