论文标题
晶格上的拓扑缺陷：二元性和脱落性
Topological Defects on the Lattice: Dualities and Degeneracies
论文作者
论文摘要
我们在二维经典晶格模型和量子链中构建拓扑缺陷。缺陷满足当地的换向关系，以确保分区函数独立于其路径。这些关系及其解决方案被扩展，以允许缺陷线融合，分支和满足融合类别的所有属性。我们展示了如何通过Turaev-Viro-Barrett-Westbury分区函数的边界条件来自然描述的二维经典晶格模型及其拓扑缺陷。这些缺陷使得Kramers-Wannier二元性可以推广到大量模型，从而解释了与非对称性相关的基态以及低能频谱之间的确切归化性。它们给出了扭曲边界条件和dehn曲折的普遍行为的精确而普遍的概念。将拓扑缺陷粘贴到边界上会产生不同边界条件的分区函数之间的线性身份，从而使通用G因子的比率可以精确地在晶格上计算。我们在各种示例中详细介绍了这种结构，包括Potts，Parafermion和高度模型。
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.
