广义弦网模型：一个彻底的阐述
Generalized string-net models: A thorough exposition
摘要：
我们描述了如何构建广义弦网模型，一类完全可解的晶格模型，实现了一个大家庭的二维拓扑有序的物质相。这些模型的基态可以被认为是不同的“弦网配置”的叠加，其中每个弦网配置是在$xy$平面中绘制的具有标记边缘的三价图。使这个结构比原来的弦网结构更一般的是，与原来的结构不同，四面体反射对称性没有被假设，也没有假设基态波函数$Φ$是“各向同性的”：即在一般化的设置中，两个可以连续变形成另一个的弦网结构$X_1, X_2$可以有不同的基态振幅，$Φ(X_1) \neq Φ(X_2)$。因此，广义弦网模型可以实现原始结构无法实现的拓扑相。在本文中，我们提供了一个更详细的讨论的基态波函数，哈密顿量，和最小的自洽条件的广义弦网络模型比现有的文献。我们还展示了如何构建字符串操作符，创建任意子在这些模型中的激发，我们展示了如何计算这些激发的编织统计。最后，我们得到了必要和充分的条件，广义弦网络模型有各向同性的基态波函数的平面或球-属性，可能是有用的，在某些应用中。
英文摘要：
We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of 2D topologically ordered phases of matter. The ground states of these models can be thought of as superpositions of different "string-net configurations", where each string-net configuration is a trivalent graph with labeled edges, drawn in the $xy$ plane. What makes this construction more general than the original string-net construction is that, unlike the original construction, tetrahedral reflection symmetry is not assumed, nor is it assumed that the ground state wave function $Φ$ is "isotropic": i.e. in the generalized setup, two string-net configurations $X_1, X_2$ that can be continuously deformed into one another can have different ground state amplitudes, $Φ(X_1) \neq Φ(X_2)$. As a result, generalized string-net models can realize topological phases that are inaccessible to the original construction. In this paper, we provide a more detailed discussion of ground state wave functions, Hamiltonians, and minimal self-consistency conditions for generalized string-net models than what exists in the previous literature. We also show how to construct string operators that create anyon excitations in these models, and we show how to compute the braiding statistics of these excitations. Finally, we derive necessary and sufficient conditions for generalized string-net models to have isotropic ground state wave functions on the plane or the sphere -- a property that may be useful in some applications.
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。
