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We study a generic model of a Chern insulator supplemented by a Hubbardinteraction in arbitrary even dimension $D$ and demonstrate that the modelremains well-defined and nontrivial in the $D \to \infty$ limit. Dynamicalmean-field theory is applicable and predicts a phase diagram with a continuumof topologically different phases separating a correlated Mott insulator fromthe trivial band insulator. We discuss various features, such as the elusivedistinction between insulating and semi-metal states, which are unconventionalalready in the non-interacting case. Topological phases are characterized by anon-quantized Chern density replacing the Chern number as $D\to \infty$.

Interacting Chern Insulator in Infinite Spatial Dimensions