Binary-coupling sparse SYK model: spectral form factor and scrambling dynamics

Masaki Tezuka^1*

¹Department of Physics, Kyoto University, Kyoto, Japan

* Presenter:Masaki Tezuka, email:tezuka@scphys.kyoto-u.ac.jp

The Sachdev-Ye-Kitaev (SYK) model, proposed in 2015, is a quantum mechanical model of N Majorana or complex fermions with all-to-all random interactions. The model has attracted significant attention over the years due to its features such as the existence of the large-N solution with maximally chaotic behavior at low temperatures and holographic correspondence to a low-dimensional gravity theory.
The sparse version of the SYK model reproduces essential feature of the original model for reduced numbers of disorder parameters. We recently proposed [1] a further simplification, which is to set the nonzero couplings to be ±1, rather than sampling from a continuous distribution such as Gaussian. This binary-coupling model exhibits strong correlations in the energy spectrum, as observed in the spectral form factor, more efficiently in terms of the number of nonzero terms than in the Gaussian distribution case. We also comment on the scrambling dynamics with the binary-coupling sparse SYK model, comparing the model with other variants of SYK.
[1] M. Tezuka, O. Oktay, E. Rinaldi, M. Hanada, and F. Nori, arXiv:2208.12098.

Keywords: Sachdev-Ye-Kitaev model, quantum chaos, information scrambling