Effects of Electron Correlations on Hofstadter Spectrum

TL;DR

This paper derives a modified Harper's equation to study how electron-electron interactions influence the Hofstadter spectrum, revealing changes in band gaps and widths but preserving self-similarity and fractal characteristics.

Contribution

It introduces a new theoretical framework for analyzing electron correlations' effects on the Hofstadter spectrum, extending previous non-interacting models.

Findings

Band gaps and widths are modified by electron correlations.

Self-similarity and Cantor set structure remain unchanged.

Theoretical model provides insights into correlated electron systems.

Abstract

By allowing interactions between electrons, a new Harper's equation is derived to examine the effects of electron correlations on the Hofstadter energy spectra. It is shown that the structure of the Hofstadter butterfly ofr the system of correlated electrons is modified only in the band gaps and the band widths, but not in the characteristics of self-similarity and the Cantor set.