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

by Soshun Ozaki (University of Tokyo)

Tuesday 4 Feb 2025, 11:00 → 12:00 Europe/Zurich

WHGA/121

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 by the proposal of the Sachdev-Ye-Kitaev (SYK) model [1,2] as a toy model holographically dual to a 1+1-dimensional black hole. The SYK model, consisting of Majorana fermions with four-body random interactions, is regarded as a canonical example of quantum many-body chaos due to its random matrix-like spectrum and the presence of Lyapunov exponents in out-of-time-order correlators (OTOCs).
In this talk, we introduce two disorder-free, integrable variants of the SYK model, which we refer to as clean SYK model, demonstrate their integrability, and analyze their static and dynamical properties. Using the obtained analytical solutions, we show that the OTOCs in these models exhibit exponential-like growth at early times [3], resembling the behavior of many-body quantum chaotic systems, despite their large N behavior differing from typical chaotic systems. As expected, however, our analysis finds no evidence of random-matrix behavior in the level statistics or spectral form factor, reflecting the integrable nature of these models. These findings suggest that the clean SYK models provide simple yet nontrivial examples of disorder-free quantum many-body systems exhibiting partially chaos-like behavior in their 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.