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Fractional quantum Hall states at zero magnetic field


Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures that arise in tight-binding Hamiltonians defined on hexagonal, square, and kagome lattices with staggered fluxes. We then present a simple prescription to flatten isolated Bloch bands with non-zero Chern number, thus mimicking a Landau level. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.