标题： 熵序参数在二维共形场论中的分类对称性 显示英文标题

标题： Entropic Order Parameters for Categorical Symmetries in 2D-CFT

摘要： 在本工作中，我们提出了一种信息论的序参数，能够表征(1 + 1)-d 有理共形场理论（RCFT）中分类对称性的存在和破缺。 具体而言，我们计算了代表具有分类对称性理论的不同对称性破缺相之间相变临界点的RCFT基态之间的量子相对熵，以及它们的对称化版本。 我们发现，在高温极限的领先阶次下，这种相对熵仅依赖于实现分类对称性的拓扑算符的量子维度的期望值。 这种依赖关系表明，我们的提议可以用于表征(1 + 1)-d 具有分类对称性理论的不同破缺相。 显示英文摘要

摘要： In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (1 + 1)-d rational conformal field theories (RCFT). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of (1 + 1)-d theories with categorical symmetries.