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

In this work, we investigate the quantum chaos in various $T\bar{T}$-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.