Reply to Comment on "Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model"

TL;DR

This paper refutes a recent claim by demonstrating that the perturbative approach used is invalid in the parameter range, and confirms a chaotic-integrable transition in the SYK model that challenges previous conclusions.

Contribution

It clarifies the limitations of the perturbative formalism and establishes the existence of a chaotic-integrable transition in the SYK model.

Findings

Perturbative formalism breaks down in the parameter range of interest.

The model exhibits a chaotic-integrable transition for large fixed N.

Previous claims of always positive Lyapunov exponent are invalidated.

Abstract

In a recent comment to the paper Chaotic Integrable transition in the SYK model, it was claimed that, in a certain region of parameters, the Lyapunov exponent of the N Majoranas Sachdev-Ye-Kitaev model with a quadratic perturbation, is always positive. This implies that the model is quantum chaotic. In this reply, we show that the employed perturbative formalism breaks down precisely in the range of parameters investigated in the comment due to a lack of separation of time scales. Moreover, based on recent analytical results, we show that for any large and fixed N, the model has indeed a chaotic-integrable transition that invalidate the results of the comment.