Minimal Multifractality in the Spectrum of a Quasiperiodic Hamiltonian

TL;DR

This paper demonstrates that the energy spectrum of a quasiperiodic Hamiltonian can exhibit minimal multifractality by tuning system parameters, simplifying the analysis of multiscaling effects in such systems.

Contribution

It introduces a method to achieve minimal multifractality in the spectrum of a quasiperiodic Hamiltonian through parameter tuning based on trace map analysis.

Findings

Minimal multifractality achieved at specific parameter tuning.

Wave packet diffusion reflects reduced intermittency.

Simplifies analysis of multiscaling in quasiperiodic systems.

Abstract

In many systems, the electronic energy spectrum is a continuous or singular continuous multifractal set with a distribution of scaling exponents. Here, we show that for a quasiperiodic potential, the multifractal energy spectrum can have a minimal dispersion of the scaling exponents. This is made by tuning the ratio between self-energies in a tigth-binding Hamiltonian defined in a quasiperiodic Fibonacci chain. The tuning is calculated numerically from a trace map, and coincides with the place where the scaling exponents of the map, obtained from cycles with period six and two, are equal. The diffusion of electronic wave packets also reflects the minimal multifractal fractal nature of the spectrum, by reducing intermittency. The present result can help to simplify the task of studying several problems in quasiperiodic systems, since the effects of multiscaling are better isolated.