We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for N ≤ 26 Majorana fermions with q-body interaction with $q=4,6,8$ for a range of sparse parameter k. Using the peak of the Krylov complexity as a probe, we find change in behavior as we vary k for various q. We argue that this captures the change from holographic to non-holographic behavior in the sparse SYK-type models such that model is holographic for all k ≥ kₘᵢₙ. Our results also indicate that the Krylov complexity peak has a holographic interpretation similar to the Lyapunov exponent.
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Jha et al. (2024) studied this question.
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