A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.

中文翻译：

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二次Sachdev-Ye-Kitaev模型中的指数斜坡

频谱形状因数的长期线性增长提供了对中间时间的量子混沌的普遍诊断。相比之下，在无序可积多体模型中频谱形状因子的行为还不是很清楚。在这里，我们研究了两体Sachdev-Ye-Kitaev模型，并表明光谱形状因子具有指数斜率，与混沌模型中的线性斜率形成鲜明对比。我们在频谱形状因子的路径积分公式中根据鞍点的高维流形找到了一种针对这种指数斜坡的新颖机制。之所以出现这种流形，是因为该理论具有很大的对称性。由于有限的不可积分的相互作用强度，这些微妙的对称性减少到相对的时间平移，从而使指数斜率让位于线性斜率。