Magnetic Fingerprints of Fractal Spectra and Duality of Hofstadter Models

TL;DR

This paper investigates the fractal spectral properties of the Hofstadter model through magnetization oscillations, revealing thermodynamic signatures of fractality and elucidating the model's duality transformation.

Contribution

It introduces a detailed analysis of de-Haas van Alphen oscillations in the Hofstadter model, highlighting their role as thermodynamic fingerprints of fractal spectra and clarifying the duality transformation.

Findings

Magnetization oscillations exhibit lip-shaped envelopes near split bands.

Fractal properties manifest as oscillation structures on all scales.

Duality of the Hofstadter model is clarified through magnetization analysis.

Abstract

We study the de-Haas van Alphen oscillations in the magnetization of the Hofstadter model. Near a split band the magnetization is a rapidly oscillating function of the Fermi energy with lip shaped envelopes. For generic magnetic fields this structure appears on all scales and provides a thermodynamic fingerprint of the fractal properties of the model. The analysis applies equally well to the two dual interpretations of the Hofstadter model and the nature of the duality transformation is elucidated.