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We study the Hubbard model with flat bands in the presence of magnetic flux or spin-orbit coupling. We provide two different constructions of the tight binding model with flat bands separated from the other ones by a finite gap. In the first construction, the flat band is non-topological, i.e., the Chern number of it is trivial. By considering the on-site Coulomb repulsion, we rigorously show that the many-body ground states are ferromagnetic when this flat band is half-filled. On the other hand, in the second construction, we consider the tight- binding model embedded on a thin torus. In this case, the flat band can be topological. Furthermore, we show rigorously that the ground states are quantum Hall ferromagnets. |
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