Level-Statistics of Disordered Systems: a Single Parametric Formulation

TL;DR

This paper demonstrates that the level statistics of disordered systems at the metal-insulator transition can be described by a single parametric formulation similar to Brownian ensembles, providing analytical insights into critical behavior.

Contribution

It introduces a unified single parametric model for level statistics in disordered systems, linking them to Brownian ensembles and enabling analysis of critical point correlations.

Findings

Level statistics follow a single parametric form during transition.

Analytical evidence supports single parameter scaling behavior.

The model applies across various disorder strengths.

Abstract

We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders behaves in a way similar to that of the single parametric Brownian ensembles. The latter appear during aPoisson $\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling behaviour in disordered systems as well as a tool to obtain the level-correlations at the critical point for a wide range of disorders.