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

TL;DR

This paper demonstrates that extended self-similarity, a concept from turbulence, also applies to the two-dimensional metal-insulator transition, revealing universal scaling behaviors across different physical systems.

Contribution

It establishes the presence of extended self-similarity in the 2D metal-insulator transition and offers a phenomenological interpretation within the random β-model framework.

Findings

Extended self-similarity observed in the metal-insulator transition.

Deviations from multifractality linked to finite size effects.

Verification of extended self-similarity in strange attractors.

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 $\beta$-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.