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.
Highlights
Ð1Þ for a fixed and large N, T=κ ≪ 1, J=κ ≪ 1
According to Ref. [1], the dynamics is quantum chaotic for a sufficiently large κ assuming the rest of parameters (T, N, J) are fixed
This is in tension with the results of Ref. [2] where we show that, for T, N, J fixed, this model is only quantum chaotic for sufficiently small κ
Summary
Ð1Þ for a fixed and large N, T=κ ≪ 1, J=κ ≪ 1. [1], the dynamics is quantum chaotic for a sufficiently large κ assuming the rest of parameters (T, N, J) are fixed. This is in tension with the results of Ref.
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