根单位 XXZ 链中的可移动缝：相对通量类与反幺正谱配对
Movable seams in root-of-unity XXZ chains: Relative flux classes and antiunitary spectral pairing
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中文总结 AI 辅助
在根单位 XXZ 链中构造可移动缝，通过反幺正对称性保护相对通量类，导致偶数重数谱配对，并区分局部规范不可见的全局通量。
中文摘要 AI 辅助
从 Vernier、Miao 和 Yamazaki（VMY）引入的循环对偶张量出发，其端点迹矩阵乘积算符满足 $\mathbb Z_N$ Tambara--Yamagami 融合，并实现紧致玻色子共形场论中的拓扑缺陷线。我们保留虚拟端点作为 $N$ 态动力学自由度，在 $q=\mathrm e^{\mathrm iπM/N}$ 且 $\gcd(M,N)=1$ 的自旋-$\tfrac12$ XXZ 链中构造了一个精确可移动的缝。局部移动恒等式对任何幺正 $q$-Weyl 对成立；在有限循环实现中，所有输出相位局部规范等价，并共享相同的四个缝本征值。在环上，输出规范变为单键上的定向扭转，而端点共轭将 $2N$ 个标签简化为两个相对 $\mathbb Z_2$ 通量类。一个显式的反幺正对称性保护类 $η\equiv M-1\pmod 2$：对于偶数 $N$，它等谱地配对不同的电荷扇区，而对于奇数 $N$，它固定一个扇区并在该处平方为 $-I$。因此，受保护类中的每个多体能谱本征空间具有偶数重数。源值 $η_{\rm VMY}=1-M$ 对每个互素根满足此条件，而未规范值 $η=0$ 仅对奇数 $M$ 满足。精确的有限尺寸控制表明，相反类可以包含简单能级，因此局部规范等价不可见的全局通量在谱上区分了这两个类。
英文摘要
Starting from the cyclic duality tensors introduced by Vernier, Miao, and Yamazaki (VMY), whose endpoint-traced matrix-product operators obey $\mathbb Z_N$ Tambara--Yamagami fusion and realize topological defect lines of the compactified-boson conformal field theory, we retain the virtual endpoint as an $N$-state dynamical degree of freedom and construct an exactly movable seam in the spin-$\tfrac12$ XXZ chain at $q=\mathrm e^{\mathrm iπM/N}$ with $\gcd(M,N)=1$. The local movement identity holds for any unitary $q$-Weyl pair; in the finite cyclic realization, all output phases are locally gauge equivalent and share the same four seam eigenvalues. On a ring, the output gauge becomes a directed twist on a single bond, while endpoint conjugacy reduces the $2N$ labels to two relative $\mathbb Z_2$ flux classes. An explicit antiunitary symmetry protects the class $η\equiv M-1\pmod 2$: for even $N$ it pairs distinct charge sectors isospectrally, whereas for odd $N$ it fixes one sector and squares to $-I$ there. Hence every many-body energy eigenspace in the protected class has even multiplicity. The source value $η_{\rm VMY}=1-M$ satisfies this condition for every coprime root, whereas the ungauged value $η=0$ does so only for odd $M$. Exact finite-size controls show that the opposite class can contain simple levels, so a global flux invisible to local gauge equivalence distinguishes the two classes spectrally.
发表机构
- School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）
- Shanghai Key Laboratory of Particle Physics and Cosmology（上海粒子物理与宇宙学重点实验室）
- School of Physics, East China University of Science and Technology（华东理工大学物理系）
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