Non-Abelian hybrid fracton orders
Non-Abelian hybrid fracton orders
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DOI：
10.1103/physrevb.104.115117
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发表时间：
2021-06
影响因子：
3.7
通讯作者：
Nathanan Tantivasadakarn;Wenjie Ji;S. Vijay
中科院分区：
文献类型：
--
作者：
Nathanan Tantivasadakarn;Wenjie Ji;S. Vijay
我们介绍格点规范理论，描述三维的，有间隙的量子相位表现出传统的三维拓扑秩序和分形秩序的现象，从一个有限的G$，一个阿贝尔正常子群的选择$N$，和选择的叶状结构。这些混合分数阶（arXiv：2102.09555中介绍了它们的例子）也可以包含非阿贝尔的固定的点状激发，因此产生了受保护的简并。我们构建可解的晶格模型，这些订单之间的传统的，三维G$规范理论和纯分形阶插值，通过不同的选择正常子群$N$。我们证明了拓扑激发及其迁移率的某些通用数据与$G$和$N$的选择直接相关，并且还提出了关于这些顺序的补充观点：某些阶数可以通过测量富集特定分数子阶数的全局对称性，通过对具有受限迁移率的激发进行分数化或置换，而某些混合阶可以通过在初始解耦的二维拓扑阶的堆叠中凝聚激励来获得。
We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders, starting from a finite group $G$, a choice of an Abelian normal subgroup $N$, and a choice of foliation structure. These hybrid fracton orders -- examples of which were introduced in arXiv:2102.09555 -- can also host immobile, point-like excitations that are non-Abelian, and therefore give rise to a protected degeneracy. We construct solvable lattice models for these orders which interpolate between a conventional, three-dimensional $G$ gauge theory and a pure fracton order, by varying the choice of normal subgroup $N$. We demonstrate that certain universal data of the topological excitations and their mobilities are directly related to the choice of $G$ and $N$, and also present complementary perspectives on these orders: certain orders may be obtained by gauging a global symmetry which enriches a particular fracton order, by either fractionalizing on or permuting the excitations with restricted mobility, while certain hybrid orders can be obtained by condensing excitations in a stack of initially decoupled, two-dimensional topological orders.