Perturbative Approach to Flat Chern Bands in the Hofstadter Model

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.

40 pages, 15 figures; v2 includes minor changes, additional references and an expanded background section

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Quantum Hall Effect in Optical Lattices
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• SU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms
• Adiabatic continuity between Hofstadter and Chern insulator states
• D-Algebra Structure of Topological Insulators

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• Topological multi-mode waveguide QED
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Bosonic Fractional Quantum Hall States on a Finite Cylinder
• Fractional Chern insulators with a non-Landau level continuum limit
• Josephson Coupled Moore-Read States
• Emergent Fermi sea in a system of interacting bosons
• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
• Hofstadter-Hubbard model with opposite magnetic fields: Bardeen-Cooper-Schrieffer pairing and superfluidity in the nearly flat butterfly bands
• Emergent Fracton Hydrodynamics of Ultracold Atoms in Partially Filled Landau Levels
• Superconductivity in a Topological Lattice Model with Strong Repulsion
• Light-Matter interactions in Hofstadter lattice with the next-nearest neighbor couplings
• Gauge fields induced by curved spacetime
• Theory of Hofstadter Superconductors
• Topological quantum electrodynamics in synthetic non-Abelian gauge fields
• Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model