发表机构
Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明混合态的单点和两点关联函数可完全确定连续连通群作用的强对称性及其特征标，并提出从两点关联提取最大强对称子李群的算法，适用于凝聚态、量子模拟器等实验系统。
AI 中文摘要
强对称与弱对称及其自发破缺区分了混合态中对称性与有序的不同形式。我们证明，完整的单点和两点关联函数（等价于所有两格点约化密度矩阵）能确定连续局域酉作用下连通群的精确强对称性：具有相同关联的态具有相同的强对称性及其特征标。我们还提出一种算法，从两点关联函数中确定最大连通强对称子李群及其特征标。由于此类关联比全态层析更易获取，该算法可直接应用于从凝聚态系统到量子模拟器和量子电路等各类实验。我们还识别了某些群和表示特例，在这些情况下，更少的关联函数就足够。
英文摘要
Strong and weak symmetries and their spontaneous breaking distinguish different forms of symmetry and order in mixed states. We show that complete one- and two-point correlation functions, equivalently all two-site reduced density matrices, determine exact strong symmetry for continuous onsite unitary actions of connected groups: states with identical correlations have the same strong symmetry and character. We also present an algorithm to determine the maximal connected strong-symmetry sub-Lie group and its character from two-point correlations. Because such correlations are more accessible than full-state tomography, the algorithm is readily applicable to experiments ranging from condensed-matter systems to quantum simulators and circuits. We also identify group and representation-specific cases in which fewer correlations suffice.
Comments6 pages, 1 figure
