### 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.

Original language | English (US) |
---|---|

Article number | 021014 |

Journal | Physical Review X |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1 2011 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Fractional Chern Insulator'. Together they form a unique fingerprint.

## Cite this

*Physical Review X*,

*1*(2), [021014]. https://doi.org/10.1103/PhysRevX.1.021014