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. Numerical diagonalization of the model Hamiltonian gives much insight into the dynamics of the model. We have studied (i) the spectral correlation by computing the spectral form factor [1], and (ii) the scrambling dynamics of the model by using the Hayden-Preskill protocol [2]. In addition to the result for the original SYK model, we present the results for the binary-coupling sparse SYK model [3] and the SYK4+2 model [4].

Reference:
[1] J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, JHEP 1705:118 (2017) [arXiv:1611.04650]; H. Gharibyan, M. Hanada, S. H. Shenker, and M. Tezuka, JHEP 1807:124 (2018) [arXiv:1803.08050].
[2] P. Hayden and J. Preskill, JHEP 0709:120 (2007) [arXiv:0708.4025].
[3] M. Tezuka, O. Oktay, E. Rinaldi, M. Hanada, and E. Nori, arXiv:2208.12098.
[4] A. M. García-García, B. Loureiro, A. Romero-Bermúdez, and M. Tezuka, Phys. Rev. Lett. 120, 241603 (2018) [arXiv:1707.02197].

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