AI 中文总结
本文通过临界Ising链的Kramers-Wannier对偶缺陷，证明其量子维度d_sigma=sqrt(2)编码在基态单粒子纠缠谱中，马约拉纳零模产生边界熵log g=(1/2)log 2，并给出对偶扭曲基态的两个独立解读。
AI 中文摘要
非可逆对称性由无理量子维度的拓扑缺陷表征，但其对量子多体态纠缠的影响尚未在谱层面得到解析。我们证明典型例子——临界Ising链的Kramers--Wannier (KW)对偶缺陷（量子维度d_sigma=sqrt(2)）的范畴数据编码在其基态的单粒子纠缠谱中：一个最大混合的马约拉纳零模是边界熵log g=(1/2)log 2的谱起源，因此也是d_sigma本身的起源。沿两条独立路径解读同一对偶扭曲基态——转移矩阵动量偏移和能量的卡西米尔曲率——两次确定扭曲场权重h_sigma=1/16，缺陷希尔伯特空间组织成半整数sigma扭曲共形塔。这将边界熵从积分数量提升为可逆性的能级分辨谱特征，并为缺乏自由费米子捷径的对偶缺陷的张量网络研究提供了精确可解的校准目标。
英文摘要
A non-invertible topological line fixes global defect data but does not select a reduced density matrix (RDM) in a spatially twisted sector. For the Kramers-Wannier defect of the critical Ising chain, we choose the equal-weight incoherent mixture of the two charge-sector ground states and reduce it to the ordinary full spin algebra of a complete non-wrapping prefix anchored at the defect endpoint. The finite-size RDM is the convex average of two charge-sector RDMs rather than a sign-zero Gaussian proxy, and an exact descended antiunitary enforces many-body Kramers pairing without determining the entropy. At fixed prefix, the RDMs converge in trace norm to a common Gaussian state as the circumference grows. Convergence is uniform over all ground-doublet preparations, including coherent pure states. The subsequent large-prefix entropy limit follows from the odd-even Toeplitz/Fisher-Hartwig endpoint, yielding half the natural logarithm of two above the homogeneous chain. The matched spin-flip defect has zero excess. The exact joint energy-modified-translation character of the same twisted Hamiltonian records the finite-size roots and their multiplicities, retains chirality in the marked scaling limit, and, using the standard Ising character identities, resolves the four Virasoro towers of the Ising duality-twisted sector.
Comments66 pages, 4 figures. Revised version. Code: https://doi.org/10.5281/zenodo.21523746
