Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging

Rodriguez, Alberto; Vasquez, Louella J.; Roemer, Rudolf A.

Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging

Authors

Rodriguez, Alberto

Vasquez, Louella J.

Roemer, Rudolf A.

Description

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 $f(α)$ is numerically obtained using the \textsl{ensemble 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 typical average of the scaling law. System-size scaling with ensemble average appears as the most adequate method to carry out the numerical MFA. Some conjectures about the true shape of $f(α)$ in the thermodynamic limit are also made.
10 pages, 13 figures