Multifractal analysis of the metal-insulator transition in the 3D Anderson model
We study the multifractal analysis (MFA) of electronic wavefunctions at the localisation-delocalisation transition in the 3D Anderson model for very large system sizes up to 240^3. The singularity spectrum f(alpha) is numerically obtained using the ensemble and the typical average of the scaling law for the generalized inverse participation ratios $P_q$, employing box-size and system-size scaling. The validity of a recently reported symmetry law [Phys. Rev. Lett. 97, 046803 (2006)] for the multifractal spectrum is carefully analysed at the metal-insulator transition (MIT). The results are compared to those obtained using different approaches, in particular the box- and system-size scaling approaches. System-size scaling with ensemble average appears as the most adequate method to carry out the numerical MFA.