Many Body Localization in a Two Dimensional Itinerant SYK Model

We consider a two dimensional itinerant SYK model of spin-less fermions, with a linear dispersion, interacting via random long range all-to-all interactions. In the large-N limit, we find an asymptotic power series solution of the saddle-point equations, which demonstrate that the SYK interactions drive the formation of localized states in the strong coupling regime. By calculating the current-current correlation function, the ground state is shown to be insulating. Finally, we calculate the out-of-time-correlator (OTOC), which has a $t$-linear growth in time and an associated logarithmic growth of entanglement; thereby proving that the system forms a many body localized phase.