Translational symmetry breaking and the disintegration of the Hofstadter butterfly

TL;DR

This paper investigates how interactions in a honeycomb lattice cause charge ordering that breaks symmetries, leading to the disintegration of the Hofstadter butterfly fractal pattern and affecting Hall conductivity and Landau fan diagrams.

Contribution

It demonstrates that interactions induce symmetry-breaking phase transitions that fragment the Hofstadter butterfly, revealing new length scales and altered topological properties.

Findings

Charge ordering breaks translational and rotational symmetries.

Disintegration of the Hofstadter butterfly increases with interaction strength.

Hall conductivity and Landau fan diagrams are affected by these phase transitions.

Abstract

We study the effect of interactions on the Hofstadter butterfly of the honeycomb lattice. We show that the interactions induce charge ordering that breaks the translational and rotational symmetries of the system. These phase transitions are prolific and occur at many values of the flux and particle density. The breaking of the translational symmetry introduces a new length scale in the problem and this affects the energy band diagram resulting in the disintegration of the fractal structure in the energy flux plot, the Hofstadter butterfly. This disintegration increases with increase in the interaction strength. Many of these phase transitions are accompanied with change in the Hall conductivity. Consequently, the disintegration of the Hofstadter butterfly is manifested in the Landau fan diagram also.