论文标题
带有HOPF代数量规理论的通量附件的修改复曲面代码模型
Modified toric code models with flux attachment from Hopf algebra gauge theory
论文作者
论文摘要
Kitaev的曲折代码是使用仪表理论的有限规组构建的。可以通过将量规组推广到任何有限维半密码霍普夫代数的量规组进行概括。这也导致了复曲面代码的概括。在这里，我们考虑了仪表组不变但配有非平凡的准二轴结构（R-Matrix）的简单情况，该结构（R-Matrix）修改了规格理论的构建。这导致了一些有趣的现象。例如，组上的函数空间变成了非共同代数。我们还获得了简单的汉密尔顿模型，概括了紫色代码，这些模型与感谢您的代码具有相同的总体拓扑类型，只是将模型中字符串算子创建的各种粒子以取决于r-matrix的方式排列。在$ \ mathbb {z} _ {n} $量规理论的情况下，我们发现引入非平凡的R-Matrix等于磁通附件。
Kitaev's toric code is constructed using a finite gauge group from gauge theory. Such gauge theories can be generalized with the gauge group generalized to any finite-dimensional semisimple Hopf algebra. This also leads to generalizations of the toric code. Here we consider the simple case where the gauge group is unchanged but furnished with a non-trivial quasitriangular structure (R-matrix), which modifies the construction of the gauge theory. This leads to some interesting phenomena; for example, the space of functions on the group becomes a non-commutative algebra. We also obtain simple Hamiltonian models generalizing the toric code, which are of the same overall topological type as the toric code, except that the various species of particles created by string operators in the model are permuted in a way that depends on the R-matrix. In the case of $\mathbb{Z}_{N}$ gauge theory, we find that the introduction of a non-trivial R-matrix amounts to flux attachment.
