Model Fractional Chern Insulators

Abstract

We devise local lattice models whose ground states are model fractional Chern insulators---Abelian and non-Abelian topologically ordered states characterized by exact ground state degeneracies at any finite size and infinite entanglement gaps. Most saliently, we construct exact parent Hamiltonians for two distinct families of bosonic lattice generalizations of the ${\mathcal{Z}}_k$ parafermion quantum Hall states: (i) color-entangled fractional Chern insulators at band filling fractions $\nu =k/(\mathcal{C}+1)$ and (ii) nematic states at $\nu =k/2$, where $\mathcal{C}$ is the Chern number of the lowest band in our models. In spite of a fluctuating Berry curvature, our construction is partially frustration free: the ground states reside entirely within the lowest band and exactly minimize a local $(k+1)$-body repulsion term by term. In addition to providing the first known models hosting intriguing states such as higher Chern number generalizations of the Fibonacci anyon quantum Hall states, the remarkable stability and finite-size properties make our models particularly well-suited for the study of novel phenomena involving e.g. twist defects and proximity induced superconductivity, as well as being a guide for designing experiments.

9 pages, 5 figures

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Cited by in corpus (30)

• Topological Bands for Ultracold Atoms
• Topological properties of a dense atomic lattice gas
• Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Band structure engineering of ideal fractional Chern insulators
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Topological Lattice Models with Constant Berry Curvature
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• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Systematic construction of topological flat-band models by molecular-orbital representation
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• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Broken Symmetry in Ideal Chern Bands
• Dynamical topological excitations in parafermion chains
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Three-component fractional quantum Hall effect in topological flat bands
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Topological Order Without Band Topology in Moiré Graphene
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping