论文标题
散装Anyons作为边缘对称性：拓扑排序状态的边界相图
Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States
论文作者
论文摘要
我们有效地研究了一维系统，这些系统在二维拓扑秩序状态的边缘或两个拓扑排序状态之间的边界处出现。我们认为，大容量的任何人都与边缘的新兴对称性有关，这在其相图的结构中起着至关重要的作用。使用这种对称原理，可以从对称破裂的过渡或对称性受保护的拓扑阶段之间的对称性断裂过渡或过渡来理解，在阿贝尔状态边界处的不同间隙阶段之间的过渡。当批量主持非亚伯利亚人时，就会发生更多的异国情调现象。为了证明这些原理，我们探讨了图意的代码的单个和双层边缘的相图，以及单层和双层Kitaev Spin Liquid（KSL）中的域壁的相图。在KSL的情况下，我们发现批量中非亚伯利亚人的存在将Kramers-Wannier自以为是，是对有效边界理论的对称性。这些示例说明了许多令人惊讶的现象，例如自发双重性，两个扇区相变，以及在不同无间隙相之间过渡时边缘运算符的边缘运算符。
We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with emergent symmetries of the edge, which play a crucial role in the structure of its phase diagram. Using this symmetry principle, transitions between distinct gapped phases at the boundaries of Abelian states can be understood in terms of symmetry breaking transitions or transitions between symmetry protected topological phases. Yet more exotic phenomena occur when the bulk hosts non-Abelian anyons. To demonstrate these principles, we explore the phase diagrams of the edges of a single and a double layer of the toric code, as well as those of domain walls in a single and double-layer Kitaev spin liquid (KSL). In the case of the KSL, we find that the presence of a non-Abelian anyon in the bulk enforces Kramers-Wannier self-duality as a symmetry of the effective boundary theory. These examples illustrate a number of surprising phenomena, such as spontaneous duality-breaking, two-sector phase transitions, and unfreezing of marginal operators at a transition between different gapless phases.
