Analytical Results for Multifractal Properties of Spectra of Quasiperiodic Hamiltonians near the Periodic Chain

TL;DR

This paper derives analytical expressions for the multifractal properties of spectra in quasiperiodic Hamiltonians, showing their independence from incommensurability and confirming results with numerical simulations.

Contribution

It provides the first-order analytical formulas for the multifractal spectra of quasiperiodic chains, advancing understanding of their spectral properties.

Findings

Analytical expressions match numerical simulations.

Multifractal properties are independent of incommensurability.

First-order results reveal universal spectral features.

Abstract

The multifractal properties of the electronic spectrum of a general quasiperiodic chain are studied in first order in the quasiperiodic potential strength. Analytical expressions for the generalized dimensions are found and are in good agreement with numerical simulations. These first order results do not depend on the irrational incommensurability.