Numerical studies of Anderson transition

TL;DR

This paper presents numerical analysis of the Anderson transition in 3D and 4D, focusing on the statistics of eigenvalues of the transfer matrix and their behavior at critical points, revealing universal features.

Contribution

It provides new numerical evidence for the behavior of eigenvalue statistics at the Anderson transition, including the linear density at criticality and universal forms in the insulating regime.

Findings

Linear eigenvalue density at criticality in 3D proven and discussed

Universal form of eigenvalue density found in insulating regime

Density change describes crossover from metallic to localized regime

Abstract

We present numerical results for the statistics of $z$'s ($z$'s are defined as logarithm of eigenvalues of the transfermatrix $T^\dag T$) at the critical points of Anderson transition in 3D and 4D. The change of the density of $z$ due to the crossover from the metallic to the localized regime is described. Linear behavior $\rho(z)= z$ at the critical point in 3D is proven and discussed. In the insulating regime, the universal form of $\rho$ has been found.