One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions

TL;DR

This paper introduces a new superuniversal scaling relation for spectral statistics in three-dimensional disordered systems, unifying different symmetry classes and supporting the existence of one-parameter scaling at the metal-insulator transition.

Contribution

It presents a novel superuniversal scaling relation that collapses spectral data across symmetry classes, providing evidence for one-parameter scaling in the metal-insulator transition.

Findings

Data collapse onto a single scaling curve for all symmetry classes

Evidence supporting one-parameter scaling at the transition

Proposal of a family of spacing distribution functions $P_g(s)$

Abstract

Based on the spectral statistics obtained in numerical simulations on three dimensional disordered systems within the tight--binding approximation, a new superuniversal scaling relation is presented that allows us to collapse data for the orthogonal, unitary and symplectic symmetry ($\beta=1,2,4$) onto a single scaling curve. This relation provides a strong evidence for one-parameter scaling existing in these systems which exhibit a second order phase transition. As a result a possible one-parameter family of spacing distribution functions, $P_g(s)$, is given for each symmetry class $\beta$, where $g$ is the dimensionless conductance.