Topological defects on the lattice: I. The Ising model
Topological defects on the lattice: I. The Ising model
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DOI：
10.1088/1751-8113/49/35/354001
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发表时间：
2016-01
期刊：
影响因子：
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通讯作者：
D. Aasen;R. Mong;P. Fendley
中科院分区：
文献类型：
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作者：
D. Aasen;R. Mong;P. Fendley
在本文及其后续工作中，我们构造了二维经典晶格模型和量子自旋链中的拓扑不变缺陷。我们展示了缺陷线如何与传输矩阵/哈密顿函数交换，当它们服从缺陷交换关系时，杨-巴克斯特方程的表兄弟。这些关系和它们的解可以被扩展以允许缺陷线分支和融合，同样具有仅取决于拓扑的性质。在第一部分中，我们集中讨论最简单的例子，伊辛模型。我们定义了晶格自旋翻转和对偶缺陷及其分支，并证明了它们是拓扑的。一个有用的结果是一个简单的实施Kramers-Wannier对偶环面和更高的亏格表面通过使用融合的对偶缺陷。我们使用这些拓扑缺陷做简单的计算，产生精确的性质的共形场理论描述的连续极限。例如，在对偶扭曲边界条件下动量量子化的位移产生手征自旋场的共形自旋1/16。更令人惊讶的是，我们得到的模块化转换矩阵明确和准确。
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang–Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers–Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.