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arXiv · 2609.27940

Movable seams in root-of-unity XXZ chains: Relative flux classes and antiunitary spectral pairing

Boliang Yu·Ruixin Zhou·Meisen Gao
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Abstract

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.

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Boliang Yu, Ruixin Zhou, Meisen Gao. 2026-08-24. Movable seams in root-of-unity XXZ chains: Relative flux classes and antiunitary spectral pairing. https://arxiv.org/abs/2609.27940

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