On the critical level-curvature distribution

TL;DR

This paper investigates the distribution of energy level curvatures at the Anderson localization critical point, revealing a universal power-law tail and a hybrid distribution that connects localization and quantum diffusion, with relevance to experimental observations.

Contribution

It introduces a critical level-curvature distribution for a quasiperiodic ring, showing universal features and connecting to the Anderson model and experiments.

Findings

Distribution has a |K|^{-3} tail for large curvatures.

Overall distribution is close to log-normal, indicating localization.

Resembles the critical distribution of the disordered Anderson model.

Abstract

The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a critical distribution which has the universal random matrix theory form ${\bar P}(K)\sim |K|^{-3}$ for large level-curvatures $|K|$ corresponding to quantum diffusion, although overall it is close to approximate log-normal statistics corresponding to localization. The obtained hybrid distribution resembles the critical distribution of the disordered Anderson model and makes a connection to recent experimental data.