Anderson transition in systems with chiral symmetry

TL;DR

This paper explores how chiral symmetry influences Anderson localization in three-dimensional disordered systems, revealing that it induces an Anderson transition near the band center and affects critical properties like multifractality.

Contribution

It demonstrates that chiral symmetry causes an Anderson transition in 3D disordered systems and analyzes its impact on critical phenomena and eigenstate decay.

Findings

Chiral symmetry induces an Anderson transition near the band center.

Critical properties such as multifractality are quantitatively affected by chiral symmetry.

The transition is linked to power-law decay of eigenstates.

Abstract

Anderson localization is a universal quantum feature caused by destructive interference. On the other hand chiral symmetry is a key ingredient in different problems of theoretical physics: from nonperturbative QCD to highly doped semiconductors. We investigate the interplay of these two phenomena in the context of a three-dimensional disordered system. We show that chiral symmetry induces an Anderson transition (AT) in the region close to the band center. Typical properties at the AT such as multifractality and critical statistics are quantitatively affected by this additional symmetry. The origin of the AT has been traced back to the power-law decay of the eigenstates; this feature may also be relevant in systems without chiral symmetry.