Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane

Abstract

We study the Sachdev-Ye-Kitaev (SYK4) model with a weak SYK2 term of magnitude Γ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, J/NΓJ/N, fluctuations of the Schwarzian mode are suppressed, and the SYK4 mean-field solution remains valid beyond the timescale t0∼N/J up to t∗∼J/Γ2. The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2πT, but its prefactor scales as T at low temperatures T≤Γ.