Two-local modifications of Sachdev-Ye-Kitaev model with quantum chaos

The Sachdev-Ye-Kitaev (SYK) model may provide us with a good starting point for the experimental study of quantum chaos and holography in the laboratory. Still, the four-local interaction of fermions makes quantum simulation challenging, and it would be good to search for simpler models that keep the essence. In this paper, we argue that the four-local interaction may not be important by introducing a few models that have two-local interactions. The first model is a generalization of the spin-SYK model, which is obtained by replacing the spin variables with SU(d) generators. Simulations of this class of models might be straightforward on qudit-based quantum devices. We study the case of d=3,4,5,6 numerically and observe quantum chaos already for two-local interactions in a wide energy range. We also introduce modifications of spin-SYK and SYK models that have similar structures as the SU(d) model (e.g., H=∑_{p,q}J_{pq}χ_{p}χ_{p+1}χ_{q}χ_{q+1} instead of the original SYK Hamiltonian H=∑_{p,q,r,s}J_{pqrs}χ_{p}χ_{q}χ_{r}χ_{s}), which shows strongly chaotic features although the interaction is essentially two-local. These models may be a good starting point for the quantum simulation of the original SYK model.