Extended Self-Similarity in the Two-Dimensional Metal-Insulator Transition

Abstract

We show that extended self-similarity, a scaling phenomenon firstly observed in classical turbulent flows, holds for a two-dimensional metal-insulator transition that belongs to the universality class of random Dirac fermions. Deviations from multifractality, which in turbulence are due to the dominance of diffusive processes at small scales, appear in the condensed matter context as a large scale, finite size effect related to the imposition of an infra-red cutoff in the field theory formulation. We propose a phenomenological interpretation of extended self-similarity in the metal-insulator transition within the framework of the random $β$-model description of multifractal sets. As a natural step our discussion is bridged to the analysis of strange attractors, where crossovers between multifractal and non-multifractal regimes are found and extended self-similarity turns to be verified as well.