# Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model

García-García, Antonio M. (Shanghai Center for Complex Physics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China) ; Loureiro, Bruno (TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom) ; Romero-Bermúdez, Aurelio (Instituut-Lorentz for Theoretical Physics ΔITP, Leiden University, Niels Bohrweg 2, Leiden 2333CA, The Netherlands) ; Tezuka, Masaki (Department of Physics, Kyoto University, Kyoto 606-8502, Japan)

15 June 2018

Abstract: 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.

Published in: Physical Review Letters 120 (2018)