Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition

TL;DR

This study numerically investigates the level spacing distribution at the Anderson transition, revealing a size-independent asymptotic form and estimating the correlation length exponent through high-precision calculations.

Contribution

It introduces a new interpolation of the critical cumulative probability with a universal asymptotic form at the Anderson transition.

Findings

Asymptotic form ^{-s^{\u03b1}} with  .1

Correlation length exponent estimated from scaling behavior

Size-independent critical cumulative probability conjectured

Abstract

The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is examined for large spacings near the delocalization-localization transition and the correlation length exponent is found. By using high-precision calculations we conjecture a new interpolation of the critical cumulative probability, which has size-independent asymptotic form \ln I(s) \propto -s^{\alpha} with \alpha = 1.0 \pm 0.1.