The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality, and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with a different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a nonchaotic Fermi liquid sits at the critical point with an equal number of modes. At a finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at a finite temperature. We characterize the phase diagram in terms of the spectral function, the Lyapunov exponent, and the entropy. Our results illustrate a concrete example of the quantum phase transition and critical behavior between two non-Fermi liquid phases.

中文翻译：

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二次耦合Sachdev-Ye-Kitaev模型中混沌和非混沌相之间的竞争

Sachdev-Ye-Kitaev（SYK）模型是一个可求解的具体模型，用于研究非费米液体特性，全息对偶性和最大混沌行为。在这项工作中，我们考虑了SYK模型的一般化，该模型包含两个SYK模型，它们具有不同数量的Majorana模式，并通过二次项耦合。该模型也是可解的，解决方案显示了两个非费米液体混沌相之间的零温度量子相变。通过调整两个模式数的比率来驱动此相变，并且非混沌费米液体位于具有相同模式数的临界点。在有限的温度下，费米液相膨胀至有限的状态。更有趣的是，在有限的温度下会出现不同的非费米液相。我们用频谱函数来表征相图，李雅普诺夫指数和熵 我们的结果说明了两个非费米液相之间的量子相变和临界行为的具体示例。