Level statistics and localization in a 2D quantum percolation problem

TL;DR

This study investigates how quantum states in a 2D percolation model transition from localized to delocalized, revealing a strong correlation between level statistics and the percolation threshold.

Contribution

It introduces a numerical analysis of level statistics and localization in a 2D quantum percolation model with variable tunneling range, highlighting the crossover behaviors.

Findings

Maximum level repulsion occurs near the percolation threshold.

A crossover from GOE to Poisson level statistics is observed.

A transition from localized to delocalized states is identified.

Abstract

A two dimensional model for quantum percolation with variable tunneling range is studied. For this purpose the Lifshitz model is considered where the disorder enters the Hamiltonian via the nondiagonal elements. We employ a numerical method to analyze the level statistics of this model. It turns out that the level repulsion is strongest around the percolation threshold. As we go away from the maximum level repulsion a crossover from a GOE type behavior to a Poisson like distribution is indicated. The localization properties are calculated by using the sensitivity to boundary conditions and we find a strong crossover from localized to delocalized states.