Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane
A. V. Lunkin, Alexei Kitaev, M. V. Feigel’man
Abstract
We study the Sachdev-Ye-Kitaev (${\mathrm{SYK}}_{4}$) model with a weak ${\mathrm{SYK}}_{2}$ term of magnitude $\mathrm{\ensuremath{\Gamma}}$ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, $J/N\ensuremath{\ll}\mathrm{\ensuremath{\Gamma}}\ensuremath{\ll}J/\sqrt{N}$, fluctuations of the Schwarzian mode are suppressed, and the ${\mathrm{SYK}}_{4}$ mean-field solution remains valid beyond the timescale ${t}_{0}\ensuremath{\sim}N/J$ up to ${t}_{*}\ensuremath{\sim}J/{\mathrm{\ensuremath{\Gamma}}}^{2}$. The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent $2\ensuremath{\pi}T$, but its prefactor scales as $T$ at low temperatures $T\ensuremath{\le}\mathrm{\ensuremath{\Gamma}}$.