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Integrability and Braided Tensor Categories
Journal of Statistical Physics ( IF 1.6 ) Pub Date : 2021-02-18 , DOI: 10.1007/s10955-021-02712-6
Paul Fendley

Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on the Boltzmann weights admitting a conserved current, generalising one found using quantum-group algebras. The resulting trigonometric weights are typically those of a critical integrable lattice model, so the method here gives a linear way of “Baxterising”, i.e. building a solution of the Yang-Baxter equation out of topological data. It also illuminates why many models do not admit a solution. I discuss many examples in geometric and local models, including (perhaps) a new solution.



中文翻译:

可积性和编织张量类别

许多可积分统计力学模型具有分数自旋守恒电流。通过利用量子群代数和“离散全纯性”的思想来构造这样的电流。我自然而然地发现它们是使用编织张量类别,由结不变式,正因和共形场理论产生的拓扑结构。我推导了一个关于守恒电流的玻尔兹曼权重的简单约束条件,归纳了使用量子群代数发现的一个广义电流。所得的三角权重通常是关键可积晶格模型的三角权重,因此此处的方法给出了“ Baxterising”的线性方式,即从拓扑数据中构建Yang-Baxter方程的解。这也说明了为什么许多模型不接受解决方案。我讨论了几何模型和局部模型中的许多示例,

更新日期:2021-02-18
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