发表机构
Harbin Normal University; Great Bay University; California State University Northridge（哈尔滨师范大学; 大湾区大学; 北岭加州州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过DMRG计算在自旋-1方格模型中发现了非阿贝尔手征自旋液体相，证实Moore-Read态的存在，为高自旋系统拓扑量子计算提供新平台。
AI 中文摘要
非阿贝尔手征自旋液体（CSLs）承载非阿贝尔任意子激发，是拓扑量子计算的有前景平台。然而，在短程相互作用的自旋系统中实现非阿贝尔CSL仍然难以实现。在此，我们研究了一个自旋-1方格模型，包含最近邻和次近邻双线性相互作用（$J_1,J_2$）以及双二次相互作用（$K_1,K_2$），还有三自旋标量手征耦合$J_{\chi}$。受精确对角化和无限投影纠缠对态计算中Moore-Read态证据的启发，我们固定$J_1=1.0$，$J_2/J_1=0.623$，$K_1/J_1=-0.176$，并使用密度矩阵重正化群（DMRG）计算获得了$0 \leq K_2/J_1 \leq 0.4$和$0.3 \leq J_{\chi}/J_1 \leq 0.6$范围内的量子相图。我们识别出条纹反铁磁相、Néel反铁磁相、磁有序手征自旋态相，以及在有序相边界附近出现的非阿贝尔CSL相。无偏的DMRG结果为Moore-Read态提供了强有力的证据，包括三个拓扑扇区、量子化的自旋陈数$C=1$，以及低能纠缠谱的能级计数，这与手征SU(2)$_2$共形场论一致。我们的结果可能为在其他具有短程耦合的高自旋（$S > 1/2$）系统中寻找非阿贝尔CSL提供新的启示。
英文摘要
Non-Abelian chiral spin liquids (CSLs) host non-Abelian anyon excitations and are promising platforms for topological quantum computation. However, realizing non-Abelian CSLs in short-range interacting spin systems remains elusive. Here, we study a spin-$1$ square-lattice model with the first- and second-neighbor bilinear ($J_1,J_2$) and biquadratic interactions ($K_1,K_2$), as well as the three-spin scalar chiral coupling $J_χ$. Inspired by the evidence of the Moore-Read state in exact diagonalization and infinite Projected Entangled Pair States calculations, we fix $J_1=1.0$, $J_2/J_1=0.623$, $K_1/J_1=-0.176$, and obtain a quantum phase diagram for $0 \leq K_2/J_1 \leq 0.4$ and $0.3 \leq J_χ/J_1 \leq 0.6$ by using the density matrix renormalization group (DMRG) calculations. We identify a stripe antiferromagnetic phase, a Néel antiferromagnetic phase, a magnetically ordered chiral spin state phase, and a non-Abelian CSL phase emerging near the boundaries of the ordered phases. The unbiased DMRG results provide strong evidence for the Moore-Read state, including the three topological sectors, the quantized spin Chern number $C=1$, and the level counting of low-lying entanglement spectra which is consistent with the chiral SU(2)$_2$ conformal field theory. Our results may shed new light on searching for non-Abelian CSLs in other higher-spin ($S > 1/2$) systems with short-range couplings.
Comments11 pages, 9 figures
