A new class of SYK-like models with maximal chaos

TL;DR

This paper introduces a new class of SYK-like models involving Majorana fermions and bosons, revealing maximal chaos and conformal properties, extending understanding of strongly correlated quantum systems.

Contribution

It proposes a novel SYK-like model with auxiliary bosons, analyzes its conformal dimensions, and demonstrates maximal chaos across different parameter regimes.

Findings

Model exhibits two conformal branches with distinct dimensions.

Maximal chaos is achieved regardless of the ratio M/N.

Supersymmetric saddle point exists at M=N.

Abstract

We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the $\mathcal{N}=1$ supersymmetric SYK model. It consists of $N$ real Majorana fermions and $M$ auxiliary bosons with Yukawa interactions. We consider the large $N$ and $M$ limit and keep the ratio $M/N$ fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio $M/N$. One of the branches contains the supersymmetric saddle for $M=N$. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of $M/N$.