AI 中文总结
本文针对周期非厄米Baxter-Fendley $Z_N$时钟链，利用算子值匹配多项式求解其有限尺寸谱，提出牛顿延拓法高效计算基态能量，还揭示了边界诱导临界性的相关判据。
AI 中文摘要
周期非厄米Baxter-Fendley $Z_N$时钟链一直缺乏完整的有限尺寸谱解，而其开链对应模型可通过独立准能求解。对于周期模型，我们证明与其循环Weyl代数相关的算子值匹配多项式同时生成一组守恒量（包括哈密顿量），并实现循环$\tau^{(2)}$杨-巴克斯特转移矩阵。单位根闭合在每个电荷区产生有限的多项式谱方程组，其可复现按代数重数计数的完整有限尺寸能谱。作为该结果的首个应用，我们证明这些方程的牛顿延拓提供了无需枚举全谱即可求解周期基态能量的实用数值途径。对于均匀链，热力学 seam响应给出边界诱导临界性的判据；当$N=3$时，其预测存在两个具有奇异基态曲率的互易临界耦合，与单一自对偶开边界临界点形成对比。
英文摘要
The periodic non-Hermitian Baxter-Fendley $Z_N$ clock chain has lacked a complete finite-size spectral solution, whereas its open-chain counterpart admits a solution in terms of independent quasienergies. For the periodic model we show that the operator-valued matching polynomial associated with its cyclic Weyl algebra simultaneously generates a set of conserved quantities, including the Hamiltonian, and realizes a cyclic $τ^{(2)}$ Yang-Baxter transfer matrix. Root-of-unity closure yields a finite system of polynomial spectral equations in each charge sector, which reproduces the complete finite-size energy spectrum counted with algebraic multiplicity. As a first application of this result, we show that Newton continuation of these equations provides a practical numerical route to the periodic ground-state energy without enumerating the full spectrum. For homogeneous chains the thermodynamic seam response yields a criterion for boundary-induced criticality; for $N=3$ it predicts two reciprocal critical couplings with singular ground-state curvature, in contrast to the single self-dual open boundary critical point.
Comments8 pages, 2 figues, plus Supplemental Material
