Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$

Abstract

We study the stability of composite fermion fractional quantum Hall states in Harper-Hofstadter bands with Chern number $|C|>1$. We analyze the states of the composite fermion series for bosons with contact interactions and (spinless) fermions with nearest-neighbor interactions. We examine the scaling of the many-body gap as the bands are tuned to the effective continuum limit $n_{\varphi }\to 1/|C|$. Near these points, the Hofstadter model realises large magnetic unit cells that yield bands with perfectly flat dispersion and Berry curvature. We exploit the known scaling of energies in the effective continuum limit in order to maintain a fixed square aspect ratio in finite-size calculations. Based on exact diagonalization calculations of the band-projected Hamiltonian, we show that almost all finite-size spectra yield the ground-state degeneracy predicted by composite fermion theory. We confirm that states at low ranks in the composite fermion hierarchy are the most robust and yield a clear gap in the thermodynamic limit. For bosons in $|C|=2$ and $|C|=3$ bands, our data for the composite fermion states are compatible with a finite gap in the thermodynamic limit. We also report new evidence for gapped incompressible states of fermions in $|C|>1$ bands, which have large entanglement gaps. For cases with a clear spectral gap, we confirm that the thermodynamic limit commutes with the effective continuum limit. We analyze the nature of the correlation functions for the Abelian composite fermion states and find that they feature $|C{|}^2$ smooth sheets. We examine two cases associated with a bosonic integer quantum Hall effect (BIQHE): For $\nu =2$ in $|C|=1$ bands, we find a strong competing state with a higher ground-state degeneracy, so no clear BIQHE is found in the band-projected Hofstadter model; for $\nu =1$ in $|C|=2$ bands, we present additional data confirming the existence of a BIQHE state.

25 pages, 24 figures

References in corpus (26)

• Photovoltaic Hall effect in graphene
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Nearly-flat bands with nontrivial topology
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Fractional quantum Hall effect in the absence of Landau levels
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Optical lattice quantum Hall effect
• Spinful Composite Fermions in a Negative Effective Field
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Adiabatic continuity between Hofstadter and Chern insulator states
• Condensed Groundstates of Frustrated Bose-Hubbard Models
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Continuous Preparation of a Fractional Chern Insulator
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Characterization of topological states on a lattice with Chern number
• Competing Compressible and Incompressible Phases in Rotating Atomic Bose Gases at Filling Factor $\nu =2$
• Josephson Coupled Moore-Read States

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