Many-body localization in a finite-range Sachdev-Ye-Kitaev model and holography

We study level statistics of a generalized Sachdev-Ye-Kitaev (SYK) model with two-body and one-body random interactions of finite range by exact diagonalization. Tuning the range of the one-body term, while keeping the two-body interaction sufficiently long ranged, does not alter substantially the spectral correlations, which are still given by the random matrix prediction typical of a quantum chaotic system. However, a transition to an insulating state, characterized by Poisson statistics, is observed by reducing the range of the two-body interaction. Close to the many-body metal-insulator transition, we show that spectral correlations share all features previously found in systems at the Anderson transition and in the proximity of the many-body localization transition. Our results suggest the potential relevance of SYK models in the context of many-body localization. It also offers a starting point for the exploration of a gravity dual of this phenomenon which we speculate to be related to the Hawking-Page transition.