We prove that all the criteria proposed in the literature to identify a Chern band hosting exact fractional Chern insulating ground states, in fact, describe an equivalence with a lowest Landau level defined in curved space under a nonuniform magnetic field. In addition, we design an operational test for the most general instance of such lowest Landau-level mapping, which only relies on the computationally inexpensive evaluation of Bloch wavefunctions' derivatives. Our work clarifies the common origin of various Chern-idealness criteria, proves that these criteria exhaust all possible lowest Landau levels, and hints at classes of Chern bands that may possess interesting phases beyond Landaulevel physics.

中文翻译：

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弯曲空间中朗道能级的理想陈氏能带

我们证明，文献中提出的用于识别具有精确分数陈绝缘基态的陈能带的所有标准，实际上描述了在非均匀磁场下的弯曲空间中定义的最低朗道能级的等价性。此外，我们还为此类最低朗道级映射的最一般实例设计了一个操作测试，该测试仅依赖于对布洛赫波函数导数的计算成本低廉的评估。我们的工作阐明了各种陈理想性标准的共同起源，证明这些标准耗尽了所有可能的最低朗道能级，并暗示了可能拥有超出朗道级物理的有趣相的陈能带类别。