Fracton Models on General Three-Dimensional Manifolds
Fracton Models on General Three-Dimensional Manifolds
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DOI：
10.1103/physrevx.8.031051
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发表时间：
2017-12
影响因子：
12.5
通讯作者：
Wilbur E. Shirley;K. Slagle;Zhenghan Wang;Xie Chen
中科院分区：
文献类型：
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作者：
Wilbur E. Shirley;K. Slagle;Zhenghan Wang;Xie Chen
Fracton模型是最近在三个空间尺寸中发现的异国情调的格子晶格汉密尔顿人的集合，它包含一些“拓扑”特征：它们支持分数散装激发（称为分裂），以及对局部扰动的强大基础状态退化。但是，由于仅在具有周期性边界条件的立方晶格上定义和分析了先前的Fracton模型，因此尚不清楚拓扑概念在多大程度上适用。在本文中，我们证明了X-Cube模型是一种原型I型Fracton模型，可以在一般的三维流形上定义。我们的构造围绕着空间歧管的奇异紧凑型总叶叶的概念，该叶子构造了一个相交的平行表面相交堆栈的晶格，称为叶子。我们发现基态脱落率取决于叶子的拓扑结构和叶片相交的模式。我们进一步表明，可以从X-Cube模型的重新归一化组变换中理解这种依赖性，其中可以通过添加或删除拓扑状态的2D层来更改系统大小。我们的结果导致了对分裂阶段的定义的改进，并提高了分形式顺序的拓扑性质。
Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some 'topological' features: they support fractional bulk excitations (dubbed fractons), and a ground state degeneracy that is robust to local perturbations. However, because previous fracton models have only been defined and analyzed on a cubic lattice with periodic boundary conditions, it is unclear to what extent a notion of topology is applicable. In this paper, we demonstrate that the X-cube model, a prototypical type-I fracton model, can be defined on general three-dimensional manifolds. Our construction revolves around the notion of a singular compact total foliation of the spatial manifold, which constructs a lattice from intersecting stacks of parallel surfaces called leaves. We find that the ground state degeneracy depends on the topology of the leaves and the pattern of leaf intersections. We further show that such a dependence can be understood from a renormalization group transformation for the X-cube model, wherein the system size can be changed by adding or removing 2D layers of topological states. Our results lead to an improved definition of fracton phase and bring to the fore the topological nature of fracton orders.