标题： 对具有非可逆对称性的混合态的SymTFT方法 显示英文标题

标题： SymTFT Approach for Mixed States with Non-Invertible Symmetries

摘要： 我们开发了一个通用框架，用于研究具有强对称性和弱对称性的混合态相，包括非可逆或范畴对称性。 核心思想是考虑混合态密度矩阵的纯化，该纯化存在于一个加倍的希尔伯特空间中。 我们提出了在这一加倍希尔伯特空间中相的系统分类，这关键地依赖于对称拓扑场理论（SymTFT）方法。 该框架不仅适用于群对称性，而且重要的是，也适用于非可逆对称性。 我们在1+1d中说明了该方法，用于分类具有强（非）可逆对称性的相，这些相包括从强到弱的自发对称性破缺（SWSSB）相和混合强/弱对称性保护的拓扑相（SPT）。 我们还开发了一种研究涉及强对称性和弱对称性组合的对称性的方法。 一个值得注意的例子是具有弱非可逆Kramers-Wannier对偶对称性和强$\mathbb{Z}_2$对称性的例子。 连续描述由基于SymTFT框架的格点模型分析补充。 显示英文摘要

摘要： We develop a general framework for studying phases of mixed states with strong and weak symmetries, including non-invertible or categorical symmetries. The central idea is to consider a purification of the mixed state density matrix, which lives in a doubled Hilbert space. We propose a systematic classification of phases in this doubled Hilbert space, relying crucially on the Symmetry Topological Field Theory (SymTFT) approach. This framework applies not only to group symmetries but also, importantly, to non-invertible symmetries. We illustrate the approach in 1+1d to classify phases with strong (non-)invertible symmetries, which include strong-to-weak spontaneous symmetry breaking (SWSSB) phases and mixed strong/weak symmetry-protected topological phases (SPTs). We also develop an approach for studying symmetries that involve a combination of strong and weak symmetries. A noteworthy example of this has weak non-invertible Kramers-Wannier duality symmetry and strong $\mathbb{Z}_2$ symmetry. The continuum description is complemented by a lattice model analysis informed by the SymTFT framework.