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Series of Abelian and non-Abelian states in C ＞ 1 fractional Chern insulators

机译：C＞ 1分数Chern绝缘子的Abelian和非Abelian状态序列

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摘要

We report the observation of a series of Abelian and non-Abelian topological states in fractional Chern insulators (FCIs). The states appear at bosonic filling v = k/(C + 1)(k,C integers) in several lattice models, in fractionally filled bands of Chern numbers C ≥ 1 subject to on-site Hubbard interactions. We show strong evidence that the k = 1 series is Abelian while the k ＞ 1 series is non-Abelian. The energy spectrum at both ground-state filling and upon the addition of quasiholes shows a low-lying manifold of states whose total degeneracy and counting matches, at the appropriate size, that of the fractional quantum Hall (FQH) SU(C) (color) singlet k-clustered states (including Halperin, non-Abelian spin singlet states and their generalizations). The ground-state momenta are correctly predicted by the FQH to FCI lattice folding. However, the counting of FCI states also matches that of a spinless FQH series, preventing a clear identification just from the energy spectrum. The entanglement spectrum lends support to the identification of our states as SU(C) color singlets, but offers anomalies in the counting for C ＞ 1, possibly related to dislocations that call for the development of alternative counting rules of these topological states.
机译：我们报告分数分数绝缘子（FCIs）中一系列阿贝尔和非阿贝尔拓扑状态的观察。这些状态出现在几个晶格模型中的玻色填充v = k /（C +1）（k，C整数）处，在受实哈伯德相互作用的情况下，在Chern数C≥1的分数填充带中。我们显示出有力的证据，证明k = 1系列是Abelian，而k＞ 1系列是非Abelian。在基态填充和添加准空穴时的能谱显示出一个低洼状态的状态，其总简并和计数在适当的大小上与分数量子霍尔（FQH）SU（C）的状态相匹配（颜色）单重态k簇状态（包括Halperin，非阿贝尔自旋单重态及其概括）。通过FQH到FCI晶格折叠可以正确预测基态动量。但是，FCI状态的计数也与无旋转FQH系列的计数相匹配，从而无法从能量谱中清楚地识别。纠缠光谱有助于将我们的状态识别为SU（C）颜色单峰，但在C＞ 1的计数中提供了异常，可能与位错有关，这些位错要求开发这些拓扑状态的替代计数规则。

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