论文标题
3维复曲面代码模型中的缺陷形式形成编织的融合2类
Defects in the 3-dimensional toric code model form a braided fusion 2-category
论文作者
论文摘要
众所周知，在3维（空间维度）曲折代码模型中有$ e $零件和$ m $串，它实现了3维$ \ Mathbb {z} _2 _2 $拓扑顺序。然而，最近的数学结果表明，在3维$ \ mathbb {z} _2 $拓扑顺序中还有其他类似字符串的拓扑缺陷。在这项工作中，我们构建了Codimension 2及更高的所有拓扑缺陷，并表明它们形成了构成编织的融合2类，满足了编织的非分类条件。
It was well known that there are $e$-particles and $m$-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional $\mathbb{Z}_2$ topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional $\mathbb{Z}_2$ topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.
