Quantum chaos is one of the distinctive features of the Sachdev-Ye-Kitaev (SYK) model, $N$ Majorana fermions in $0+1$ dimensions with infinite-range two-body interactions, which is attracting a lot of interest as a toy model for holography. Here we show analytically and numerically that a generalized SYK model with an additional one-body infinite-range random interaction, which is a relevant perturbation in the infrared, is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature. However, a chaotic-integrable transition, characterized by the vanishing of the Lyapunov exponent and spectral correlations given by Poisson statistics, occurs at a temperature that depends on the strength of the perturbation. We speculate about the gravity dual of this transition.

中文翻译：

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Sachdev-Ye-Kitaev 模型中的混沌-可积跃迁

量子混沌是 Sachdev-Ye-Kitaev (SYK) 模型的显着特征之一，$ñ$马约拉纳费米子$0+1$具有无限范围的两体相互作用的尺寸，作为全息学的玩具模型引起了很多兴趣。在这里，我们通过分析和数值表明，具有附加的单体无限范围随机相互作用的广义 SYK 模型（这是红外中的相关扰动）仍然是量子混沌并且对于固定的扰动值保留其大部分全息特征和足够高的温度。然而，混沌可积跃迁，其特征是李雅普诺夫指数的消失和泊松统计给出的光谱相关性，发生在取决于扰动强度的温度下。我们推测这种转变的引力对偶。