Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large $N$ theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev model for up to $N=60$ Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators. Our procedure accurately determines the Lyapunov exponent, $\lambda$, across a wide range in temperatures, including in the regime where $\lambda$ approaches the universal bound, $\lambda =2\pi /\beta$.

中文翻译：

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Sachdev-Ye-Kitaev模型中的多体混沌

多体混沌已成为理解强相互作用量子系统中热化的强大框架。尽管最近的分析进展使我们对某些大型多体混沌的直觉更加敏锐$ñ$从理论上讲，开发精确的数值工具以探索通用哈密顿量中的这种现象已被证明具有挑战性。为此，我们利用大规模并行，无矩阵的Krylov子空间方法来计算Sachdev-Ye-Kitaev模型中的动态相关器，直到$ñ=60$马约拉纳费米子。我们首先显示出两点相关函数的数值结果在高温下与动态平均场解一致，而在低温下，有限大小的校正量由近端黑洞的精确可解动力学定量地再现。受这些结果的激励，我们开发了一种新颖的有限尺寸重新缩放程序，用于分析无序相关器的增长。我们的程序准确地确定了Lyapunov指数，$\lambda$，温度范围很广，包括 $\lambda$ 接近普遍界限 $\lambda =2\pi /\beta$。