Quantum chaos, scrambling and operator growth in TT deformed SYK models

A bstract In this work, we investigate the quantum chaos in various TT T T ¯ -deformed SYK models with finite N, including the SYK 4, the supersymmetric SYK 4, and the SYK 2 models. We numerically study the evolution of the spectral form factor (SFF), the out-of-time ordered correlator (OTOC), and the Krylov complexity. We find that the characteristic evolution of the SFF, OTOC and K-complexity of both the SYK 4 and SSYK 4 models remains unchanged under the deformation, which implies that the properties of quantum chaos is preserved. We also identify a many-body localization behavior in the deformed SYK 2 model.