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This workshop is testament to the great progress in the design of lattice hopping models with flat topological band structures of varying Chern index. Fractionally filling these bands with interacting particles has revealed various lattice analogs of fractional quantum Hall states in a setting remote from traditional electronic Landau levels. Unfortunately, many of the models with sufficiently flat bands to reveal fractionalized phases rely on physically unrealistic Hamiltonian engineering. In this talk, I will describe how a ν=1/2 fractional Chern insulator arises naturally in a two-dimensional array of uniformly driven spins interacting exclusively through dipole-dipole coupling. As a specific implementation, I will discuss the preparation and detection of synthetic gauge potentials and fractional Chern insulating states in a system composed of ultra-cold polar molecules trapped in an optical lattice. Joint work with: NY Yao, AV Gorshkov, A. Läuchli, J. Ye, MD Lukin |
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