Proposal of realizing the Sachdev-Ye-Kitaev model from a Kitaev Spin Chain

TL;DR

This paper proposes a method to realize the SYK model using a Kitaev spin chain, enabling simulation of quantum chaos in a purely bosonic system through Majorana zero modes and perturbations.

Contribution

It introduces a novel approach to simulate the SYK model in a spin chain, connecting fermionic Majorana modes with spin operators and expanding possibilities for experimental realization.

Findings

Effective SYK interactions are obtained via perturbations.

OTOC of Majorana fermions can be approximated with spin operators.

The approach facilitates simulation of fermionic SYK physics in bosonic systems.

Abstract

The Sachdev-Ye-Kitaev (SYK) model is zero-dimensional model simulating quantum chaos using interacting Majorana fermions.Previously proposals have been made to realize the SYK model in fermionic systems that can support majorana zero modes. In this work, we simulate the SYK model in a Kitaev spin chain, where zero modes also exist in the ground state from the fermionic representation of spins. By adding other interactions as perturbations, we lift the degenerate majorana zero modes and obatin an effective SYK interactions. Although the majorana fermions are nonlocal in forms of spin operators, we show that the out-of-time-ordered correlator (OTOC) of the majorana fermions can be approximately simulated in forms of spin operators. Our proposal sheds light in simulating the fermonic SKY model and the related physics in purely bosonic systems.