Fractional Chern Insulators from the nth Root of Bandstructure

Abstract

We provide a parton construction of wavefunctions and effective field theories for fractional Chern insulators. We also analyze a strong coupling expansion in lattice gauge theory that enables us to reliably map the parton gauge theory onto the microsopic Hamiltonian. We show that this strong coupling expansion is useful because of a special hierarchy of energy scales in fractional quantum Hall physics. Our procedure is illustrated using the Hofstadter model and then applied to bosons at 1/2 filling and fermions at 1/3 filling in a checkerboard lattice model recently studied numerically. Because our construction provides a more or less unique mapping from microscopic model to effective parton description, we obtain wavefunctions in the same phase as the observed fractional Chern insulators without tuning any continuous parameters.

9+3 pages, 6 figures; v2: added refs, amplified discussion of deconfinement, improved discussion of translation invariance

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Cited by in corpus (27)

• Topological Flat Band Models and Fractional Chern Insulators
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• Fractional Quantum Hall Physics in Topological Flat Bands
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• From Luttinger liquid to non-Abelian quantum Hall states
• Realizing Fractional Chern Insulators with Dipolar Spins
• Topological Flat Bands from Dipolar Spin Systems
• Fractionalized Topological Insulators
• Hierarchy of fractional Chern insulators and competing compressible states
• Computational inverse method for constructing spaces of quantum models from wave functions
• A continuous transition between fractional quantum Hall and superfluid states
• The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models
• Topological classification of quasi-periodically driven quantum systems
• Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QE{D}_3$ and anyon superfluid
• Noncommutative geometry for three-dimensional topological insulators
• Effective field theories for topological insulators by functional bosonization
• Symmetry protected fractional Chern insulators and fractional topological insulators
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Tensor network representations of parton wave functions
• Effective hydrodynamic field theory and condensation picture of topological insulators
• Edge Excitations in Fractional Chern Insulators
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Spin quantum Hall effects in a spin-1 topological paramagnet
• $Z_2$ fractionalized Chern/topological insulators in an exactly soluble correlated model
• Experimental signatures of 3d fractional topological insulators
• Mapping a fractional quantum Hall state to a fractional Chern insulator
• Invariance of topological indices under Hilbert space truncation