Scaling up the Anderson transition in random-regular graphs

TL;DR

This paper investigates the Anderson transition on random-regular graphs, revealing continuous fractal dimensions with derivative discontinuities, non-ergodic metallic phases, and critical parameters, challenging existing Gaussian Ensemble predictions.

Contribution

It provides new insights into the nature of the Anderson transition on random-regular graphs, including fractal dimension behavior and critical exponents, expanding understanding beyond traditional models.

Findings

Fractal dimensions are continuous across the transition.

Discontinuity in derivatives indicates non-ergodicity near transition.

Critical disorder W=18.2 and exponent ν=1.00 are identified.

Abstract

We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the non-ergodicity of the metal near the Anderson transition. A critical exponent $\nu = 1.00 \pm0.02$ and critical disorder $W= 18.2\pm 0.1$ are found via a scaling approach. Our data support that the predictions of the relevant Gaussian Ensemble are only recovered at zero disorder.