Non-maximal chaos in some Sachdev-Ye-Kitaev-like models

Abstract

Abstract We study the chaos exponent of some variants of the Sachdev-Ye-Kitaev (SYK) model, namely, the $$ \mathcal{N} $$ N = 1 supersymmetry (SUSY)-SYK model and its sibling, the (N|M)-SYK model which is not supersymmetric, for arbitrary interaction strength. We find that for large q the chaos exponent of these variants, as well as the SYK and the $$ \mathcal{N} $$ N = 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.