论文标题
矩阵产品运营商代数II：一级混合状态的物质阶段
Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
论文作者
论文摘要
物质拓扑阶段的分类对于理解和表征量子材料的特性至关重要。在本文中，我们研究了一维开放量子系统中物质的阶段。如果两个状态可以通过局部量子通道的浅回路转化为另一个状态，我们将两个混合状态定义为同一阶段。我们旨在了解重新归一化固定点的矩阵产品密度运算符的相图。例如，这些状态是作为二维拓扑排序状态的边界。我们首先基于C*-Weak Hopf代数建立此类国家的家庭，该代数形成了融合类别。更具体地说，我们为这些状态的重新规定程序提供明确的局部细粒度和局部粗粒量子通道。最后，我们证明由C*-HOPF代数引起的人处于微不足道的阶段。
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed states to be in the same phase if both states can be transformed into the other by a shallow circuit of local quantum channels. We aim to understand the phase diagram of matrix product density operators that are renormalization fixed points. These states arise, for example, as boundaries of two-dimensional topologically ordered states. We first construct families of such states based on C*-weak Hopf algebras, the algebras whose representations form a fusion category. More concretely, we provide explicit local fine-graining and local coarse-graining quantum channels for the renormalization procedure of these states. Finally, we prove that those arising from C*-Hopf algebras are in the trivial phase.
