Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos

Recently, there has been renewed interest in many-body quantum chaos, not only in statistical physics but also in high-energy physics and quantum information theory. This resurgence is motivated by the conjecture that black holes act as fast scramblers and the proposal of the Sachdev-Ye-Kitaev (SYK) model [1,2] as a toy model that is holographically dual to a 1+1-dimensional black hole. The SYK model, composed of Majorana fermions with four-body random interactions, is considered chaotic due to its random matrix-like spectrum and the presence of Lyapunov exponents in the out-of-time-order correlators (OTOCs). In this talk, we introduce two disorder-free, integrable variants of the SYK model and study their static and dynamical properties. Exploiting the obtained analytical solutions, we find that the OTOC shows an exponential-like growth at early times [3], which may be interpreted as a precursor of chaos. As anticipated, on the other hand, our analysis revealed no evidence of random matrix behavior in the level statistics or spectral form factor, indicating the integrable nature of these models. Our results suggest that the clean SYK models provide notable examples of disorder-free quantum many-body systems displaying chaos-like behavior of OTOCs. [1] S. Sachdev and J. Ye, Phys. Rev. Lett. 70 3339 (1993). [2] A. Kitaev, A Simple Model of Quantum Holography, KITP Program: Entanglement in Strongly-Correlated Quantum Matter, Santa Barbara, 2015. [3] S. Ozaki and H. Katsura, arXiv: 2402:13154.