A route from maximal chaoticity to integrability

Abstract: We study the chaos exponent of some variants of the Sachdev-Ye-Kitaev (SYK) model, namely, the $\Ns=1$ supersymmetry (SUSY)-SYK model and its sibling, the $(N|M)$-SYK model which is not supersymmetric in general, for arbitrary interaction strength. We find that for large $q$ the chaos exponent of these variants, as well as the SYK and the $\Ns=2$ SUSY-SYK model, all follow a single-parameter scaling law. By quantitative arguments we further make a conjecture, i.e. that the found scaling law might hold for general one-dimensional (1D) SYK-like models with large $q$. This points out a universal route from maximal chaos towards completely regular or integrable motion in the SYK model and its 1D variants.