量子自旋系统中的纽结拓扑
Knot Topology in Quantum Spin System
摘要：
纽结理论为理解生物学、化学和物理学中的拓扑问题提供了强有力的工具。本文引入纽结理论来描述量子自旋系统中的拓扑相。研究了具有长程相互作用的精确可解模型，并将量子自旋系统的Majorana模映射为不同的结和链。自旋系统的基态的拓扑性质的可视化和特征在于使用交叉和链接数，它捕获的结和链接的几何拓扑结构。能量带的交互性被突出。在有间隙的相位中，本征态曲线相互缠绕和编织，形成链接。在无隙相位中，纠缠的本征态曲线可能形成结。我们的研究结果提供了一个替代的理解阶段的量子自旋系统，并提供洞察一维拓扑相的物质。
英文摘要：
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of the phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
