标题： 高自旋多体系统中的算子增长 显示英文标题

标题： Operator growth in many-body systems of higher spins

摘要： 我们研究了具有大于$1/2$的局域自旋的多体系统中的算符增长，同时考虑了非可积和可积 regimes。具体来说，我们在自旋值为$S=1/2$、$1$和$3/2$的一维和二维 Ising 模型中计算了 Lanczos 系数，并观察到渐近线性增长$b_n \sim n$。在可积方面，我们研究了 Potts 模型，并发现平方根增长$b_n \sim \sqrt{n}$。这两个结果与通用算符增长假说的预测一致。为了分析此设置中的算符动力学，我们采用了一个由移位和时钟算符张量积构建的广义算符基，将 Pauli 字符串的概念扩展到更高的局部维度。我们进一步报告称，最近引入的 Pauli 字符串等价类形式化可以自然地扩展到此设置。该形式化方法通过识别动态隔离的中等维度算符子空间，使得可模拟的 Heisenberg 动力学得以研究。作为一个例子，我们引入了自旋为$1$的 Kitaev-Potts 模型，其中此类子空间的识别允许以低于精确对角化的计算成本进行精确时间演化。 显示英文摘要

摘要： We study operator growth in many-body systems with on-site spins larger than $1/2$, considering both non-integrable and integrable regimes. Specifically, we compute Lanczos coefficients in the one- and two-dimensional Ising models for spin values $S=1/2$, $1$, and $3/2$, and observe asymptotically linear growth $b_n \sim n$. On the integrable side, we investigate the Potts model and find square-root growth $b_n \sim \sqrt{n}$. Both results are consistent with the predictions of the Universal Operator Growth Hypothesis. To analyze operator dynamics in this setting, we employ a generalized operator basis constructed from tensor products of shift and clock operators, extending the concept of Pauli strings to higher local dimensions. We further report that the recently introduced formalism of equivalence classes of Pauli strings can be naturally extended to this setting. This formalism enables the study of simulable Heisenberg dynamics by identifying dynamically isolated operator subspaces of moderate dimensionality. As an example, we introduce the Kitaev-Potts model with spin-$1$, where the identification of such a subspace allows for exact time evolution at a computational cost lower than that of exact diagonalization.