Spectral statistics near the quantum percolation threshold

TL;DR

This paper investigates the spectral properties of a 3D quantum bond percolation system near the metal-insulator transition, identifying critical parameters and confirming universality class consistency.

Contribution

It provides the first detailed spectral analysis near the quantum percolation threshold, estimating critical probability and exponent through finite size scaling.

Findings

Critical quantum probability p_q=0.33±0.01

Critical exponent for localization length ν=1.35±0.10

Results consistent with the Anderson model universality class

Abstract

The statistical properties of spectra of a three-dimensional quantum bond percolation system is studied in the vicinity of the metal insulator transition. In order to avoid the influence of small clusters, only regions of the spectra in which the density of states is rather smooth are analyzed. Using finite size scaling hypothesis, the critical quantum probability for bond occupation is found to be $p_q=0.33\pm.01$ while the critical exponent for the divergence of the localization length is estimated as $\nu=1.35\pm.10$. This later figure is consistent with the one found within the universality class of the standard Anderson model.