经典根系揭示稳定子Rényi熵中的缺陷-结数据
Classical Root Systems Reveal Defect-Junction Data in Stabilizer Renyi Entropy
- Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
- Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg（奥格斯堡大学物理研究所电子关联与磁学中心理论物理第三系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明临界Ising链中Pauli幅度分布通过经典根系系综精确编码边界终止几何，揭示红外不动点不可见的缺陷-测量边界结信息，并为复制边界共形场论提供具体目标。
AI中文摘要：
从临界量子态提取的普适信息取决于该态被探测的方式。空间纠缠、参与统计和稳定子Rényi熵对应于不同的复制几何，并且不一定隔离相同的边界数据。我们证明，临界Ising链中Pauli幅度的完整分布携带了边界终止的精确几何指纹，区分了流向相同红外边界不动点的晶格实现。该结构由与经典根系$A$、$B$、$C$和$D$相关的离散Selberg系综组织：共享自由-自由Ising边界条件的三个开链保留了不同的$B_L$、$C_L$和$D_L$三角墙几何。标准对称破缺代表则产生矩形、钉扎和特征插入的$C$系综。它们的四个边界矩恰好包含两个独立的乘法组合，这些组合在局部端点归一化下不变。其中一个在有限秩下精确约化为基本辛特征的一个矩，并为缺陷-测量边界结振幅提供了晶格目标。条件高斯-特征定律预测其在非锁定相中的值，而在$α=4$跃迁处的精确算术有限秩结果与高斯延拓显著偏离。这些结果表明，完整的Pauli谱解析了红外边界不动点单独无法看到的边界信息，并为复制边界共形场论提供了具体目标。
英文摘要：
Universal information extracted from a critical quantum state depends on how the state is probed. Spatial entanglement, participation statistics, and stabilizer Rényi entropy correspond to different replica geometries and need not isolate the same boundary data. We show that the complete distribution of Pauli magnitudes in critical Ising chains carries an exact geometric fingerprint of boundary termination, distinguishing lattice realizations that flow to the same infrared boundary fixed point. This structure is organized by discrete Selberg ensembles associated with the classical root systems $A$, $B$, $C$, and $D$: three open chains sharing the free--free Ising boundary condition retain distinct $B_L$, $C_L$, and $D_L$ trigonometric wall geometries. The standard symmetry-breaking representatives instead produce rectangular, pinned, and character-inserted $C$ ensembles. Their four boundary moments contain exactly two independent multiplicative combinations invariant under local endpoint normalizations. One of these reduces exactly at finite rank to a moment of the fundamental symplectic character and provides a lattice target for a defect--measurement-boundary junction amplitude. A conditional Gaussian-character law predicts its values throughout the unlocked phase, while exact-arithmetic finite-rank results at the $α=4$ transition depart sharply from the Gaussian continuation. These results show that the full Pauli spectrum resolves boundary information invisible to the infrared boundary fixed point alone and provide concrete targets for replicated boundary conformal field theory.
