论文标题
三维拓扑顺序的边界状态和脱成根的量子临界点
Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
论文作者
论文摘要
我们研究原型三维拓扑顺序的边界状态，即三维$ \ mathbb {z} _2 $ toric代码。我们将在这项工作中考虑三种不同的边界状态。在包括三个基本边界的相图中，可能存在一个多临界点，该点由所谓的解义量子临界点（DQCP）捕获，并具有“易于轴”各向异性。此外，还有一个紧急的$ \ mathbb {z} _ {2，\ text {d}} $对称互换两个边界类型，它成为DQCP全局对称性的一部分。边界上出现的$ \ mathbb {z} _ {2，\ text {d}} $对称性来自散装中的表面缺陷。我们进一步找到一个带有表面拓扑顺序的大小边界，在出现的对称性下是不变的。
We study the boundary states of the archetypal three-dimensional topological order, i.e. the three-dimensional $\mathbb{Z}_2$ toric code. There are three distinct elementary types of boundary states that we will consider in this work. In the phase diagram that includes the three elementary boundaries there may exist a multi-critical point, which is captured by the so-called deconfined quantum critical point (DQCP) with an "easy-axis" anisotropy. Moreover, there is an emergent $\mathbb{Z}_{2,\text{d}}$ symmetry that swaps two of the boundary types, and it becomes part of the global symmetry of the DQCP. The emergent $\mathbb{Z}_{2,\text{d}}$ symmetry on the boundary is originated from a type of surface defect in the bulk. We further find a gapped boundary with a surface topological order that is invariant under the emergent symmetry.
