Abstract

We propose a generalisation of multifractal analysis that is applicable to the critical regime of the Anderson localisation-delocalisation transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. The method is based on a careful finite-size study of the probability density function (PDF) of wavefunction intensities. We show that the PDF itself is sufficient to fully characterise and monitor the Anderson transition. This approach could be valuable for the wealth of such wavefunction-based experimental data that is now becoming available from LDOS measurements using STM techniques and from direct imaging of ultracold gases in disordered optical lattices. Applying this technique to high-precision data for wavefunction statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent nu=1.58+-0.03, in excellent agreement with previous transfer matrix results.