论文标题
将levin-wen模型扩展到具有间隙边界连接的二维拓扑顺序
Extend The Levin-Wen Model To Two-dimensional Topological Orders With Gapped Boundary Junctions
论文作者
论文摘要
现实的材料可能具有缺陷，通常会带来具有实际应用的物质新属性。二维拓扑排序系统的边界缺陷被认为是实现拓扑量子计算的另一种方法。为了促进对这种边界缺陷的研究，在本文中，我们通过将levin-wen模型放置在磁盘上，构建了一个准确的可解决的拓扑顺序的哈密顿式拓扑顺序模型，其中边界缺陷位于磁盘上，其间隙边界通过连接将其分离为多个段。我们发现，间隙边界连接的哈密顿量的特征是两个Frobenius代数（在输入融合类别中）的形态或共同的frobenius subgebra（在输入融合类别中）刻画了连接点的两个边界段关节。我们得出了基态退化的公式和模型的明确基础。我们提出了在边界上移动和固定电荷的概念，发现它们是量子可观察的，并标记了基础。我们的模型对计算友好。
A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of realizing topological quantum computation. To facilitate the study of such boundary defects, in this paper, we construct an exactly solvable Hamiltonian model of topological orders with gapped boundary junctions, where the boundary defects reside, by placing the Levin-Wen model on a disk, whose gapped boundary is separated into multiple segments by junctions. We find that the Hamiltonian of a gapped boundary junction is characterized by either a morphism between or a common Frobenius subalgebra of the two Frobenius algebras (in the input fusion category) characetrizing the two boundary segments joint by the junction. We derive a formula of the ground state degeneracy and an explicit ground-state basis of our model. We propose the notion of mobile and immobile charges on the boundary and find that they are quantum observables and label the ground-state basis. Our model is computation friendly.
