Chaotic Integrable Transition in the Sachdev Ye Kitaev Model.
Quantum chaos is one of the distinctive features of the Sachdev Ye Kitaev (SYK) model, N Majorana fermions in 0+1 dimensions with infinite range two body interactions, which is attracting a lot of interest as a toy model for holography. Here we show analytically and numerically that a generalized SYK model with an additional one body infinite range random interaction, which is a relevant perturbation in the infrared, is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature. However, a chaotic integrable transition, characterized by the vanishing of the Lyapunov exponent and spectral correlations given by Poisson statistics, occurs at a temperature that depends on the strength of the perturbation. We speculate about the gravity dual of this transition.
Physical review letters