We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension $D$ and demonstrate that the model remains well defined and nontrivial in the $D\to \infty$ limit. Dynamical mean-field theory is applicable and predicts a phase diagram with a continuum of topologically different phases separating a correlated Mott insulator from the trivial band insulator. We discuss various features, such as the elusive distinction between insulating and semimetal states, which are unconventional already in the noninteracting case. Topological phases are characterized by a nonquantized Chern density replacing the Chern number as $D\to \infty$.

中文翻译：

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空间尺寸互作用的Chern绝缘子

我们研究了Chern绝缘子的通用模型，该模型在任意偶数维度上均由Hubbard相互作用进行了补充 $d$ 并证明该模型在 $d\to \infty$限制。动态平均场理论是适用的，它可以预测相图，该相图具有将相关的Mott绝缘子与琐碎的带状绝缘子分开的拓扑学上不同的相的连续体。我们讨论了各种特征，例如绝缘状态和半金属状态之间的难以捉摸的区别，这在非交互情况下已经是非常规的。拓扑阶段的特征是未量化的Chern密度将Chern数替换为$d\to \infty$。