We provide new insights into the Abelian and non-Abelian chiral Kitaev spin liquids on the star lattice using the recently proposed loop gas (LG) and string gas states [Lee, Kaneko, Okubo, and Kawashima, Phys. Rev. Lett. 123, 087203 (2019)]. Those are compactly represented in the language of the tensor network. By optimizing only one or two variational parameters, accurate ansatze are found in the whole phase diagram of the Kitaev model on the star lattice. In particular, the variational energy of the LG state becomes exact (within machine precision) at two limits in the model, and the criticality at one of those is analytically derived from the LG feature. It reveals that the Abelian chiral spin liquids (CSLs) are well demonstrated by the short-ranged LG whereas the non-Abelian CSLs are adiabatically connected to the critical LG where the macroscopic loops appear. Furthermore, by constructing the minimally entangled states and exploiting their entanglement spectrum and entropy, we identify the nature of anyons and the chiral edge modes in the non-Abelian phase with the Ising conformal field theory.

中文翻译：

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紧凑张量网络表示中的Abelian和非Abelian手性自旋液体

我们使用最近提出的回路气（LG）和串气态[Lee，Kaneko，Okubo和Kawashima，Phys。牧师 123，087203（2019）]。这些以张量网络的语言紧凑地表示。通过仅优化一个或两个变量参数，就可以在Kitaev模型的整个相图中在星形晶格上找到精确的麻将。特别是，LG状态的变化能在模型的两个极限处变得精确（在机器精度范围内），并且其中之一的临界值是通过LG特征解析得出的。它揭示了短程LG很好地证明了Abelian手性自旋液体（CSL），而非Abelian CSL绝热地连接到出现宏观环的临界LG。此外，通过构造最小纠缠态并利用它们的纠缠谱和熵，