Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral correlations. Based on recent progress in the application of spectral analysis to non-Hermitian quantum systems, we show that local level statistics, which probe the dynamics around the Heisenberg time, of a non-Hermitian $q$-body Sachdev-Ye-Kitev (nHSYK) model with $N$ Majorana fermions, and its chiral and complex-fermion extensions, are also well described by random matrix theory for $q>2$, while for $q=2$, they are given by the equivalent of Poisson statistics. For that comparison, we combine exact diagonalization numerical techniques with analytical results obtained for some of the random matrix spectral observables. Moreover, depending on $q$ and $N$, we identify 19 out of the 38 non-Hermitian universality classes in the nHSYK model, including those corresponding to the tenfold way. In particular, we realize explicitly 14 out of the 15 universality classes corresponding to non-pseudo-Hermitian Hamiltonians that involve universal bulk correlations of classes ${\mathrm{AI}}^{†}$ and ${\mathrm{AII}}^{†}$, beyond the Ginibre ensembles. These results provide strong evidence of striking universal features in nonunitary many-body quantum chaos, which in all cases can be captured by nHSYK models with $q>2$.

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Sachdev-Ye-Kitaev 模型在非厄米多体量子混沌中的对称性分类和普遍性

光谱相关性是研究量子多体系统动力学的有力工具。对于 Hermitian Hamiltonian，量子混沌运动与随机矩阵理论光谱相关性有关。基于光谱分析在非厄米量子系统中应用的最新进展，我们展示了非厄米量子系统的局部能级统计，它探索了海森堡时间附近的动力学。$q$-body Sachdev-Ye-Kitev (nHSYK) 模型与$ñ$马约拉纳费米子及其手性和复费米子扩展也被随机矩阵理论很好地描述为$q>2$, 而对于$q=2$，它们由等效的泊松统计给出。为了进行比较，我们将精确的对角化数值技术与一些随机矩阵光谱观测得到的分析结果相结合。此外，根据$q$和$ñ$，我们在 nHSYK 模型中识别出 38 个非厄米普适性类别中的 19 个，包括对应于十倍方式的那些。特别是，我们明确地实现了 15 个普遍性类中的 14 个，这些普遍性类对应于涉及类的普遍体相关性的非伪厄米哈密顿量${\mathrm{人工智能}}^{†}$和${Ⅱ}^{†}$，超越 Ginibre 合奏。这些结果为非统一多体量子混沌中的显着普遍特征提供了强有力的证据，在所有情况下，nHSYK 模型都可以捕捉到这些特征$q>2$.