AI 中文总结
该研究将受激伊辛链模型扩展到高局域维度，确定了双酉点的存在条件，推导了q=3模型的纠缠熵增长表达式，发现双酉点处两类纠缠熵随时间线性增长至子系统大小决定的最大值。
AI 中文摘要
我们研究广义受激伊辛链中的纠缠动力学，将模型从标准量子比特情形（局域维度 $q=2$）扩展到更高局域维度（$q > 2$）。我们确定了“双酉”点的存在，此时模型的时空对偶性允许得到精确解析解。我们的分析表明，虽然局域维度 $q=3$ 和 $q=4$ 的系统在解析上存在少数独特的双酉点，但对于 $q \ge 5$ 的系统，由于缺乏满足所需矩阵元条件的唯一受激强度，这类点不存在。利用转移矩阵方法和专门适配高维的复制技巧，我们从一类可解初态出发，推导了 $q=3$（受激玻茨型）模型中纠缠熵增长的精确表达式。我们的结果表明，在双酉点处，雷尼熵和冯·诺依曼纠缠熵均随时间线性增长，直至达到由子系统大小决定的最大值。
英文摘要
We investigate the dynamics of entanglement in a generalized version of the kicked Ising chain, extending the model from the standard qubit case (local dimension $q=2$) to higher local dimensions ($q > 2$). We identify the existence of ''dual-unitary'' points where the model's space-time duality allows for exact analytical solutions. Our analysis reveals that while a few unique dual-unitary points exist analytically for systems with local dimensions $q=3$ and $q=4$, such points do not exist for $q \ge 5$ due to the lack of a unique kicking strength that satisfies the required matrix element conditions. Utilizing the transfer matrix method and a replica trick specifically adapted for higher dimensions, we derive exact expressions for the growth of entanglement entropy in the $q=3$ (kicked Potts-type) model starting from a class of solvable initial states. Our results demonstrate that at the dual-unitary point, both Rényi and von Neumann entanglement entropies grow linearly with time until reaching a maximum value determined by the subsystem size.
Comments23 pages, 6 figures
