# Many Body Localization in a Two Dimensional Itinerant SYK Model

## TL;DR

This paper investigates a two-dimensional itinerant SYK model with long-range interactions, demonstrating that strong coupling leads to many-body localization, insulating ground state, and characteristic dynamical behaviors such as linear OTOC growth.

## Contribution

It introduces a novel 2D itinerant SYK model and shows how strong interactions induce many-body localization with specific dynamical signatures.

## Key findings

- System exhibits insulating ground state.
- OTOC shows linear growth in time.
- System demonstrates many-body localization.

## Abstract

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.