Fracton topological order via coupled layers
Fracton topological order via coupled layers
复制标题
通过耦合层的分形拓扑顺序
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
M. Hermele
中科院分区：
文献类型：
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作者：
Han Ma;E. Lake;Xie Chen;M. Hermele
在这项工作中，我们在d = 3的空间尺寸中开发了耦合层的构造。几个不同的拓扑阶段，都来自简单的d = 2个拓扑阶段的堆叠层，以及d = 3个分叉拓扑阶段的堆栈Perspective使我们能够阐明Vijay，Haah和Fu最近引入的X-Cube模型的物理，我们可以将其作为耦合的三维三维堆栈的强耦合极限获得构建了两个新模型的分形式拓扑顺序：X-Cube模型的半概括，以及通过将四个互穿X-Cube模型耦合而获得的模型，我们将其配音为“四种颜色立方体模型”。耦合通过机制被视为拓扑秩序，我们将“ p弦凝结”和“ p-membrane凝结”表示，其中用粒子兴奋构建的字符串或膜被驱动以凝结。 - 我们构建的阶段的堕落性很容易根据更熟悉的自由度进行研究。拓扑量子场理论的框架，这可能有助于获得对此类阶段的更完整理解。
In this work, we develop a coupled layer construction of fracton topological orders in d=3 spatial dimensions. These topological phases have subextensive topological ground-state degeneracy and possess excitations whose movement is restricted in interesting ways. Our coupled layer approach is used to construct several different fracton topological phases, both from stacked layers of simple d=2 topological phases and from stacks of d=3 fracton topological phases. This perspective allows us to shed light on the physics of the X-cube model recently introduced by Vijay, Haah, and Fu, which we demonstrate can be obtained as the strong-coupling limit of a coupled three-dimensional stack of toric codes. We also construct two new models of fracton topological order: a semionic generalization of the X-cube model, and a model obtained by coupling together four interpenetrating X-cube models, which we dub the ‘four color cube model”. The couplings considered lead to fracton topological orders via mechanisms we dub “p-string condensation” and “p-membrane condensation”, in which strings or membranes built from particle excitations are driven to condense. This allows the fusion properties, braiding statistics, and ground-state degeneracy of the phases we construct to be easily studied in terms of more familiar degrees of freedom. Our work raises the possibility of studying fracton topological phases from within the framework of topological quantum field theory, which may be useful for obtaining a more complete understanding of such phases.