分数阶Chern绝缘体到无Tao-Chern态的绝热路径
Adiabatic Path from Fractional Chern Insulators to the Tao-Thouless State
摘要：
鉴于量子霍尔效应从整数到分数的演变，拓扑绝缘体研究的下一个前沿是研究分数填充拓扑平带中发生的情况。一个特别紧迫的问题是，在1/3填充的Chern平带中是否存在Laughlin态的晶格类似物，称为Chern-Laughlin态。答案关键取决于电子-电子相互作用的形式，电子-电子相互作用可以产生各种竞争的基态，如劳克林态、条纹态、副费米子态和部分子态。不幸的是，由于缺乏适当的序参量，很难精确地表征作为这些候选基态中的任何一个的确切基态。在这里，我们提出，存在一个绝热路径，从分数陈绝缘体到Tao-Tao-less状态，即，在薄环面极限下的Laughlin态的根分区态可以作为Chern-Laughlin态的有效序参量。具体地说，通过设计先变换电子-电子相互作用，再取薄环极限的分段混合绝热路径，证明了具有最近邻相互作用的Chern平坦带确实可以在1/3填充时承载Chern-Laughlin态.这种方法可以推广到可能的FCI在其他一般填充的Jain序列。
英文摘要：
In view of the evolution from the integer to fractional quantum Hall effect, the next frontier in the research of topological insulators is to investigate what happens in fractionally filled topological flat bands. A particularly pressing question is if there exists the lattice analogue of the Laughlin state in the 1/3-filled Chern flat band, dubbed as the Chern-Laughlin state. The answer depends crucially on the form of the electron-electron interaction, which can generate various competing ground states such as the Laughlin, stripe/nematic, parafermion, and parton states. Unfortunately, it is difficult to precisely characterize the exact ground state as any of these candidate ground states due to the lack of appropriate order parameters. Here, we propose that the existence of an adiabatic path from fractional Chern insulators to the Tao-Thouless state, i.e., the root partition state of the Laughlin state in the thin torus limit, can serve as an effective order parameter for the Chern-Laughlin state. Specifically, by devising the piecewise hybrid adiabatic path of first transforming the electron-electron interaction and then taking the thin torus limit, it is shown that Chern flat bands with the nearest-neighbor interaction can indeed host the Chern-Laughlin state at 1/3 filling. This method can be extended to possible FCIs at other general fillings of the Jain sequence.
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