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The fractal spectrum of a charged particle on a lattice pierced by a
homogenous flux density provides bands of any Chern number. Using that
magnetic flux per plaquette is defined only modulo flux flux quantum, we
explicitly explicitly the Hofstadter problem at flux density
nφ=p/q in terms of a magnetic unit cell of q sites. We had previously demonstrated the occurrence of different types of strongly correlated phases occurring when Hofstadter bands are filled by bosons with repulsive interactions, including composite fermion states at general flux densities and variants of Halperin states found near rational flux densities. Here, we analyse the nature of these phases in the language of fractional Chern insulators, asking in particular to which extent the problem of interacting bosons in the Hofstadter bands is represented faithfully by the projection to the flattened lowest energy band. |
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