Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States

Abstract

We show how the phases of interacting particles in topological flat bands, known as fractional Chern insulators, can be adiabatically connected to incompressible fractional quantum Hall liquids in the lowest Landau-level of an externally applied magnetic field. Unlike previous evidence suggesting the similarity of these systems, our approach enables a formal proof of the equality of their topological orders, and furthermore this proof robustly extends to the thermodynamic limit. We achieve this result using the hybrid Wannier orbital basis proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] in order to construct interpolation Hamiltonians that provide continuous deformations between the two models. We illustrate the validity of our approach for the groundstate of bosons in the half filled Chern band of the Haldane model, showing that it is adiabatically connected to the $\nu =1/2$ Laughlin state of bosons in the continuum fractional quantum Hall problem.

5 pages, 4 figures; v3: minor changes, as in final published version

References in corpus (13)

• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Wannier representation of Z_2 topological insulators
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Fractional Quantum Hall Effect in Optical Lattices
• Optical Flux Lattices for Ultracold Atomic Gases
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Bipartite entanglement entropy in fractional quantum Hall states
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators

Cited by in corpus (16)

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• Correlation effects in two-dimensional topological insulators
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• 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
• Composite Fermions on a Torus
• Interacting bosons in topological optical flux lattices
• Fractional Chern Insulators in Singular Geometries
• Josephson Coupled Moore-Read States
• Impurities and Landau level mixing in a fractional quantum Hall state in a flatband lattice model
• Exact Mappings in Condensed Matter Physics