Movable seams in root-of-unity XXZ chains: Relative flux classes and antiunitary spectral pairing
Abstract
Starting from the cyclic duality tensors introduced by Vernier, Miao, and Yamazaki (VMY), whose endpoint-traced matrix-product operators obey ℤN 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-1/2 XXZ chain at q=eiπM/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 ℤ2 flux classes. An explicit antiunitary symmetry protects the class η≡ M−1pmod 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 ηVMY=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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BibTeX
@misc{yu2026movable,
title = {{Movable seams in root-of-unity XXZ chains: Relative flux classes and antiunitary spectral pairing}},
author = {Boliang Yu and Ruixin Zhou and Meisen Gao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27940},
eprint = {2609.27940},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27940},
}
RIS
TY - UNPB
TI - Movable seams in root-of-unity XXZ chains: Relative flux classes and antiunitary spectral pairing
AU - Boliang Yu
AU - Ruixin Zhou
AU - Meisen Gao
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27940
UR - https://arxiv.org/abs/2609.27940
AB - Starting from the cyclic duality tensors introduced by Vernier, Miao, and Yamazaki (VMY), whose endpoint-traced matrix-product operators obey 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-1/2 XXZ chain at q=e^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 ℤ_2 flux classes. An explicit antiunitary symmetry protects the class η≡ M−1pmod 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_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.
ER -