格上的拓扑亏损：对偶与退化
Topological Defects on the Lattice: Dualities and Degeneracies
摘要：
我们在二维经典晶格模型和量子链中构造拓扑缺陷。缺陷线满足局部对易关系，保证了配分函数与其路径无关，这些关系及其解被推广到允许缺陷线融合、分支并满足融合范畴的所有性质.我们展示了二维经典晶格模型及其拓扑缺陷如何自然地由Turaev-Viro-Barrett-Westbury配分函数的边界条件描述。这些缺陷允许Kramers-Wannier对偶性被推广到一个大类的模型，解释确切的非对称性相关的基态之间的退化，以及在低能量谱。他们给出了一个精确的和一般的概念扭曲的边界条件和Dehn扭曲下的普遍行为。将一个拓扑缺陷粘到一个边界上，可以在不同边界条件下得到配分函数之间的线性恒等式，从而可以在格点上精确地计算出普适g因子的比值。我们详细地开发了这种结构中的各种例子，包括波茨，parafermion和高度模型。
英文摘要：
We construct topological defects in two-dimensional classical lattice models and quantum chains. The defects satisfy local commutation relations guaranteeing that the partition function is independent of their path. These relations and their solutions are extended to allow defect lines to fuse, branch and satisfy all the properties of a fusion category. We show how the two-dimensional classical lattice models and their topological defects are naturally described by boundary conditions of a Turaev-Viro-Barrett-Westbury partition function. These defects allow Kramers-Wannier duality to be generalized to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. They give a precise and general notion of twisted boundary conditions and the universal behaviour under Dehn twists. Gluing a topological defect to a boundary yields linear identities between partition functions with different boundary conditions, allowing ratios of the universal g-factor to be computed exactly on the lattice. We develop this construction in detail in a variety of examples, including the Potts, parafermion and height models.
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