Dynamical Aspects of 2D Quantum Percolation

TL;DR

This paper uses advanced numerical methods to investigate the existence of extended quantum states in 2D percolation, providing evidence that such states exist below the classical percolation threshold.

Contribution

It presents the first large-scale numerical analysis supporting the existence of extended states in 2D quantum percolation for p<1, resolving a long-standing controversy.

Findings

Extended states exist in 2D quantum percolation for p<1

Finite-size scaling confirms the presence of extended states

Particle recurrence probability indicates delocalization

Abstract

The existence of a quantum percolation threshold p_q<1 in the 2D quantum site-percolation problem has been a controversial issue for a long time. By means of a highly efficient Chebyshev expansion technique we investigate numerically the time evolution of particle states on finite disordered square lattices with system sizes not reachable up to now. After a careful finite-size scaling, our results for the particle's recurrence probability and the distribution function of the local particle density give evidence that indeed extended states exist in the 2D percolation model for p<1.