A model of randomly-coupled Pauli spins

TL;DR

This paper introduces a spin-based model with all-to-all 4-local interactions, mimicking the SYK model's properties, and explores its potential for quantum simulation and insights into holography.

Contribution

The authors develop a spin model replacing Majorana fermions in the SYK model, showing strong chaos and potential for quantum simulation applications.

Findings

Model exhibits strong chaos similar to SYK

Quantitative agreement with SYK model properties

Potential for implementation in quantum devices

Abstract

We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.