CORRELATION LENGTH AND INVERSE-PARTICIPATION-RATIO EXPONENTS AND MULTIFRACTAL STRUCTURE FOR ANDERSON LOCALIZATION

We perform numerical finite-size-scaling calculations on a standard diagonally disordered tight-binding Hamiltonian, with a Gaussian site-energy distribution. We find that the localization-length exponent is =0.97 0.05. We also find that 2/=1.430.10, where 2 is the inverse-participation-ratio exponent. 2/ can also be interpreted as the fractal dimension of the critical eigenstates. Finally, by looking at higher moments of the critical wave functions, we show that they display a multifractal structure. © 1990 The American Physical Society.