Isaac Newton Institute for Mathematical Sciences

Multifractal Analysis of the 3D Anderson Model

Authors: Alberto Rodriguez (Department of Physics and Centre for Scientific Computing, University of Warwick), Louella Vasquez (Department of Physics and Centre for Scientific Computing, University of Warwick), Rudolf Roemer (Department of Physics and Centre for Scientific Computing, University of Warwick)

Abstract

We study the multifractal analysis (MFA) of electronic wavefunctions at the metal to insulator 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 typical and ensemble averages of the scaling law for the generalized inverse participation ratio, employing box-size and system-size scaling. The validity of the symmetry law in the multifractal spectrum is carefully analysed at the MIT. System-size scaling with ensemble average appears as the most adequate method to carry out the numerical MFA.