Quantum chaos, scrambling and operator growth in $$ T\overline{T} $$ deformed SYK models

In this work, we investigate the quantum chaos in various $$ T\overline{T} $$ -deformed SYK models with finite N, including the SYK4, the supersymmetric SYK4, and the SYK2 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 SYK4 and SSYK4 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 SYK2 model.