标题： 双重酉量子混沌的结构稳定性假说 显示英文标题

标题： Structural Stability Hypothesis of Dual Unitary Quantum Chaos

摘要： 具有在足够小的能量尺度上由随机矩阵理论描述的光谱相关性的系统，被认为是最一般的量子混沌系统的特征，因为它适用于多体情况，并且远离任何半经典极限。 尽管对于一般的多体系统，这一特性在分析上极其难以证明，但对于双酉电路——一种在交换空间和时间后仍保持酉的局部量子电路的特殊类别——已经获得了严格的证明。 在这里，我们考虑从双酉电路到一般量子电路时这一特性的变化，重点关注\emph{谱形因子}，即两点相关性的傅里叶变换。 我们首先进行数值调查，结果与之前的研究一致，表明在参数空间中存在一个有限区域，在该区域内双酉物理是稳定的，光谱相关性仍然由随机矩阵理论描述，尽管仅到最大的准能量尺度。 为了解释这些发现，我们开发了一个微扰展开：如果微扰理论中出现的项满足相对简单的假设集，它就能恢复随机矩阵理论的预测。 然后我们提供了数值证据和一个启发式的分析论证来支持这些假设。 显示英文摘要

摘要： Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits -- a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focussing on the \emph{spectral form factor}, i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions.