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We study the non-stabilizerness or quantum magic of the Sachdev-Ye-Kitaev ($\rm SYK$) model, a prototype example of maximally chaotic quantum matter.
- We show that the Majorana spectrum of its ground state, encoding the spreading of the state in the Majorana basis, displays a Gaussian distribution as expected for chaotic quantum many-body systems.
- We compare our results with the case of the $\rm SYK_2$ model, describing non-chaotic random free fermions, and show that the Majorana spectrum is qualitatively different in the two cases, featuring an exponential Laplace distribution for the $\rm SYK_2$ model rather than a Gaussian.
- From the spectrum we extract the Stabilizer Renyi Entropy (SRE) and show that for both models it displays a linear scaling with system size, with a prefactor that is larger for the SYK model, which has therefore higher magic.