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Electronic wave functions in disordered systems are studied within the Anderson model of localization. At the critical disorder in 3D we diagonalize very large (103 823103 823) secular matrices by means of the Lanczos algorithm. On all length scales the obtained strong spatial fluctuations of the amplitude of the eigenstates display a multifractal character, reflected in the set of generalized fractal dimensions and the singularity spectrum of the fractal measure. An analysis of 1D systems shows multifractality too, in contrast to previous claims.
Schreiber et al. (Mon,) studied this question.