Quantum localization in incommensurate tight-binding chains

TL;DR

This paper investigates quantum localization in incommensurate coupled chains, revealing a mobility edge and effects of magnetic fields on localization, using numerical analysis of the inverse participation ratio.

Contribution

It demonstrates the existence of a mobility edge and how magnetic fields influence localization in incommensurate tight-binding chains.

Findings

Existence of a mobility edge with abrupt localization transition.

Weak magnetic fields enhance localization.

Strong magnetic fields delocalize most states.

Abstract

We explore quantum localization phenomena in a system of two coupled tight-binding chains with incommensurate periods. Employing the inverse participation ratio as a measure of localization, we investigate the effects of geometric incommensurability and external magnetic fields. Numerical results reveal the existence of a mobility edge in the spectrum characterized by an abrupt onset of localization in higher-energy states. We find that localization tends to be enhanced by a weak magnetic field, whereas a strong field delocalizes most states.