Unusual localisation effects in quantum percolation

TL;DR

This paper investigates quantum percolation on cubic lattices, revealing complex localization phenomena, spectrum fragmentation, and energy-dependent thresholds, advancing understanding of metal-insulator transitions in disordered quantum systems.

Contribution

It provides a detailed analysis of quantum percolation, highlighting non-monotonic thresholds and spectrum fragmentation, using the Kernel Polynomial Method to refine previous findings.

Findings

Non-monotonic energy dependence of percolation threshold

Spectrum fragmentation into extended and localized states

Chequerboard-like wavefunction structure at band center

Abstract

We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using the Kernel Polynomial Method we refine previous studies of the metal-insulator transition and demonstrate the non-monotonic energy dependence of the quantum percolation threshold. Remarkably, the data indicates a ``fragmentation'' of the spectrum into extended and localised states. In addition, the observation of a chequerboard-like structure of the wavefunctions at the band centre can be interpreted as anomalous localisation.