论文标题
$ \ mathbb {z} _2 $在简单双曲线上拓扑订购的阶段
$\mathbb{Z}_2$ topologically ordered phases on a simple hyperbolic lattice
论文作者
论文摘要
在这项工作中，我们在一个简单的多重晶格上考虑2D $ \ MATHBB {Z} _2 $拓扑订购的阶段（$ \ Mathbb {z} _2 $ toric代码和修改的表面代码）。引入了一个2D晶格，该晶格由1D Cayley树和1D常规晶格的产品组成，我们研究了此晶格上的两个拓扑数量的$ \ Mathbb {Z} _2 _2 $拓扑订购的阶段：封闭的表面和拓扑范围的底层变性。我们发现这两个数量取决于分支的数量和开谷树的产生。我们将这些结果归因于Anyons的大量超选择部门。
In this work, we consider 2D $\mathbb{Z}_2$ topologically ordered phases ($\mathbb{Z}_2$ toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a 1D conventional lattice, we investigate two topological quantities of the $\mathbb{Z}_2$ topologically ordered phases on this lattice: the ground state degeneracy on a closed surface and the topological entanglement entropy. We find that both quantities depend on the number of branches and the generation of the Cayley tree. We attribute these results to a huge number of superselection sectors of anyons.
