标题： 在萨奇德-叶-基塔耶夫模型及其变体中的纠缠产生 显示英文标题

标题： Entanglement production in the Sachdev-Ye-Kitaev Model and its variants

摘要： 理解量子混沌系统如何产生纠缠，可以为它们的微观混沌动力学提供见解，并有助于区分不同类别的混沌行为。 使用冯·诺依曼纠缠熵，我们研究了一个非纠缠态在三个不同变种的萨奇德-叶-基塔耶夫（SYK）模型下演化的情况，这些模型包含有限数量的马约拉纳费米子$N$。 所有变种在早期时间都表现出线性纠缠增长，而在晚期时间则趋于一个与随机矩阵理论（RMT）一致的普遍值，但它们的增长速率不同。 我们将此解释为大-$N$效应，这是由于SYK和二进制SYK中费米子算符的增强非局域性，而自旋-SYK模型中的自旋算符则没有这种特性。 数值上，我们发现这些差异随着$N$的增加逐渐显现出来。 尽管所有变种都是量子混沌的，但它们的纠缠动力学反映了不同程度的混沌，并表明纠缠生成率是一种比传统测量方法更精细的混沌探测工具。 为了探究其对这些模型热化性质的影响，我们研究了两点自相关函数，发现SYK变种之间没有差异，但在$N \geq 24$中出现了与RMT预测的偏差，尤其是在指数衰减到饱和区域的过渡附近。 显示英文摘要

摘要： Understanding how quantum chaotic systems generate entanglement can provide insight into their microscopic chaotic dynamics and can help distinguish between different classes of chaotic behavior. Using von Neumann entanglement entropy, we study a nonentangled state evolved under three variants of the Sachdev-Ye-Kitaev (SYK) model with a finite number of Majorana fermions $N$. All the variants exhibit linear entanglement growth at early times, which at late times saturates to a universal value consistent with random matrix theory (RMT), but their growth rates differ. We interpret this as a large-$N$ effect, arising from the enhanced non-locality of fermionic operators in SYK and binary SYK, absent in spin operators of the spin-SYK model. Numerically, we find that these differences emerge gradually with increasing $N$. Although all variants are quantum chaotic, their entanglement dynamics reflect varying degrees of chaos and indicate that the entanglement production rate serves as a fine-grained probe of chaos beyond conventional measures. To probe its effect on thermalization properties of these models, we study the two-point autocorrelation function, finding no differences between the SYK variants, but deviations from RMT predictions for $N \geq 24$, particularly near the crossover from exponential decay to saturation regime.