Perturbative Approach to Flat Chern Bands in the Hofstadter Model

TL;DR

This paper introduces a perturbative method to analyze flat Chern bands in the Hofstadter model near rational flux, connecting lattice states to Landau levels and enabling many-body interaction calculations.

Contribution

It develops a general perturbative framework for studying Hofstadter systems close to rational flux, linking lattice eigenstates to continuum Landau levels and calculating generalized pseudopotentials.

Findings

Eigenstates resemble Landau levels near rational flux

Perturbations break rotational symmetry and match lattice symmetry

Method enables calculation of many-body properties with interactions

Abstract

We present a perturbative approach to the study of the Hofstadter model for when the amount of flux per plaquette is close to a rational fraction. Within this approximation certain eigenstates of the system are shown to be multi-component wavefunctions that connect smoothly to the Landau levels of the continuum. The perturbative corrections to these are higher Landau level contributions that break rotational invariance and allow the perturbed states to adopt the symmetry of the lattice. In the presence of interactions, this approach allows for the calculation of generalised Haldane pseudopotentials, and in turn, the many-body properties of the system. The method is sufficiently general that it can apply to a wide variety of lattices, interactions and magnetic field strengths.