Avoided Band Crossings: Tuning Metal-Insulator Transitions in Chaotic Systems

TL;DR

This paper explores how avoided band crossings in chaotic systems can induce metal-insulator transitions, localization changes, and spectral fractality, with analysis based on the kicked Harper model.

Contribution

It demonstrates the role of avoided band crossings in tuning phase transitions and spectral properties in chaotic quantum systems, extending understanding beyond traditional models.

Findings

Avoided crossings cause metal-insulator transitions.

Localization lengths and fractal dimensions are affected.

Phenomena are explained in the kicked Harper model and predicted in other systems.

Abstract

We show that avoided crossings of energy bands may give rise to a variety of phenomena such as transitions from metal to insulator and vice versa, changes in localization lengths, and changes in the fractal dimension of energy spectra. We explain the occurrence of these phenomena in the kicked Harper model under classically chaotic conditions and predict them to occur in other systems.