Binary-coupling sparse SYK model: Spectral statistics and chaotic dynamics

Abstract

The Sachdev-Ye-Kitaev (SYK) model has garnered significant attention in the past few years due to its maximally chaotic behavior at low temperatures and holographic correspondence. The sparse version of the SYK model, which reduces the number of disorder parameters while keeping the essential properties of the original model intact, has been proposed as an improvement. Recently, we further simplified the sparse SYK model by setting nonzero couplings to ±1, rather than sampling from a continuous distribution such as Gaussian [1]. In this talk, we will focus on the binary-coupling sparse SYK model, which exhibits strong correlations in the energy spectrum and is better suited for quantum simulations of quantum chaotic behavior and holographic metals. We will present our recent findings on the spectral form factor this model, comparing it with other variants of SYK. Additionally, we discuss the out-of-time-order correlators (OTOC) of the binary-coupling model and its comparison with the sparse SYK model.

[1] M. Tezuka, O. Oktay, E. Rinaldi, M. Hanada and F. Nori, Physical Review B 107, L081103 (2023) [arXiv:2208.12098].