标题： 对称性塔可：有能隙、无能隙和混合态SPT之间的等价性 显示英文标题

标题： The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed-State SPTs

摘要： 对称拓扑场理论（SymTFT），或拓扑全息，为描述物质的量子相及其相变提供了一个统一的框架。 尽管这种方法在描述$1+1$维中的有能隙和无能隙纯态相方面取得了显著成功，但其在开放量子系统中的适用性仍完全未被探索。 在本工作中，我们通过引入\textit{对称性 饼 taco}：一种在$2+1$维中的双层拓扑序，提出了 SymTFT 框架到混合态相的自然扩展，其折叠几何结构自然地包含了$1+1$维理论中的强对称性和弱对称性。 我们利用这一观点来识别一系列对应关系，包括本征无能隙对称保护拓扑相（igSPTs）与某些有能隙对称保护拓扑相之间的一一映射，以及在$1+1$维混合态中出现的igSPTs与本征平均对称保护拓扑相（iASPTs）之间的映射。 更广泛地说，我们的框架实现了对$G$对称的短程关联 Choi 态在$1+1$维中的分类，提供了一种通过 igSPTs 的局部退相干系统生成混合态对称保护拓扑相的途径，并使我们能够识别出一种新的混合态“异常”。 除了将混合态相纳入 SymTFT 范式之外，该对称性卷饼还为探索混合态量子物质中的对偶性、异常和非平衡临界性开辟了新途径。 显示英文摘要

摘要： Symmetry topological field theory (SymTFT), or topological holography, offers a unifying framework for describing quantum phases of matter and phase transitions between them. While this approach has seen remarkable success in describing gapped and gapless pure-state phases in $1+1$d, its applicability to open quantum systems remains entirely unexplored. In this work, we propose a natural extension of the SymTFT framework to mixed-state phases by introducing the \textit{symmetry taco}: a bilayer topological order in $2+1$d whose folded geometry naturally encapsulates both strong and weak symmetries of the $1+1$d theory. We use this perspective to identify a series of correspondences, including a one-to-one map between intrinsically gapless SPTs (igSPTs) and certain gapped SPTs, and a mapping between igSPTs and intrinsically average SPTs (iASPTs) arising in $1+1$d mixed states. More broadly, our framework yields a classification of short-range correlated $G$-symmetric Choi states in $1+1$d, provides a route for systematically generating mixed-state SPTs via local decoherence of igSPTs, and allows us to identify a new mixed-state ``anomaly". Besides folding in mixed-state phases into the SymTFT paradigm, the symmetry taco opens new avenues for exploring dualities, anomalies, and non-equilibrium criticality in mixed-state quantum matter.