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Topological order in a correlated Chern insulator

We study the effect of electron-electron interactions in a spinful Chern insulator. For weak on-site repulsive interactions at half-filling, the system is a weakly correlated Chern insulator adiabatically connected to the noninteracting ground state, while in the limit of infinitely strong repulsion the system is described by an effective spin model recently predicted to exhibit a chiral spin liquid ground state. In the regime of large but finite repulsion, we find an exotic gapped phase with characteristics partaking of both the noninteracting Chern insulator and the chiral spin liquid. This phase has an integer quantized Hall conductivity $2e^2/h$ and quasiparticles with electric charges that are integer multiples of the electron charge $e$, but the ground state on the torus is four-fold degenerate and quasiparticles have fractional statistics. We discuss how these unusual properties affect the outcome of a charge pumping experiment and, by deriving the topological field theory, elucidate that the topological order is of the exotic $\mathbb{Z}_2$ double-semion type.