标题： 规范理论与混合态临界性 显示英文标题

标题： Gauge theory and mixed state criticality

摘要： 在混合量子态中，对称性的概念分为两种类型：强对称性和弱对称性。 虽然弱对称性的自发对称性破缺（SSB）可以通过两点关联函数来检测，但强对称性的SSB则由Renyi-2关联函数来表征。 在本工作中，我们提出了一种方法，从格点规范理论模型的基态相图出发，构建各种强对称性的SSB相。 除了引入一种新的混合态拓扑相之外，我们还提供了它们之间的临界性模型，包括具有无能隙对称保护拓扑序的模型。 我们明确指出，格点规范理论的基态是相应混合SSB态的纯化态。 我们的构造可以应用于任何有限规范理论，并提供了一个研究混合量子相之间量子操作的框架。 显示英文摘要

摘要： In mixed quantum states, the notion of symmetry is divided into two types: strong and weak symmetry. While spontaneous symmetry breaking (SSB) for a weak symmetry is detected by two-point correlation functions, SSB for a strong symmetry is characterized by the Renyi-2 correlators. In this work, we present a way to construct various SSB phases for strong symmetries, starting from the ground state phase diagram of lattice gauge theory models. In addition to introducing a new type of mixed-state topological phases, we provide models of the criticalities between them, including those with gapless symmetry-protected topological order. We clarify that the ground states of lattice gauge theories are purified states of the corresponding mixed SSB states. Our construction can be applied to any finite gauge theory and offers a framework to study quantum operations between mixed quantum phases.