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# Fractional Chern Insulator

## Author(s): Regnault, N; Bernevig, Bogdan A

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 Abstract: Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall effect and rule out charge-density-wave states that have not been ruled out by previous studies. By diagonalizing the Hubbard interaction in the flat-band limit of these insulators, we show the following: The system is incompressible and has a 3-fold degenerate ground state whose momenta can be computed by postulating an generalized Pauli principle with no more than 1 particle in 3 consecutive orbitals. The ground-state density is constant, and equal to 1/3 in momentum space. Excitations of the system are fractional-statistics particles whose total counting matches that of quasiholes in the Laughlin state based on the same generalized Pauli principle. The entanglement spectrum of the state has a clear entanglement gap which seems to remain finite in the thermodynamic limit. The levels below the gap exhibit counting identical to that of Laughlin 1/3 quasiholes. Both the 3 ground states and excited states exhibit spectral flow upon flux insertion. All the properties above disappear in the trivial state of the insulator-both the many-body energy gap and the entanglement gap close at the phase transition when the single-particle Hamiltonian goes from topologically nontrivial to topologically trivial. These facts clearly show that fractional many-body states are possible in topological insulators. Publication Date: 2-Dec-2011 Citation: Regnault, N, Bernevig, B Andrei. (2011). Fractional Chern Insulator. PHYSICAL REVIEW X, 1 (10.1103/PhysRevX.1.021014 DOI: doi:10.1103/PhysRevX.1.021014 ISSN: 2160-3308 Type of Material: Journal Article Journal/Proceeding Title: PHYSICAL REVIEW X Version: Final published version. This is an open access article.

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