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Sparsity dependence of Krylov state complexity in the SYK model

Raghav G. Jha1,* and Ranadeep Roy2,†

  • *Contact author: raghav.govind.jha@gmail.com
  • †Contact author: ranadeep83@gmail.com
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Phys. Rev. D 112, 046017 – Published 21 August, 2025

DOI: https://doi.org/10.1103/qsyk-m3sg

Abstract

We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for N≤28 Majorana fermions with q-body fermion interaction with q=4, 6, 8 for a range of sparse parameter k that controls the number of remaining terms in the original SYK model after sparsification. The critical value of k below which the model ceases to be holographic, denoted kc, has been subject of several recent investigations. Using Krylov complexity as a probe, we find that the peak value of complexity does not change as we increase k beyond k≥kmin at large temperatures. We argue that this behavior is related to the change in the holographic nature of the Hamiltonian in the sparse SYK-type models such that the model is holographic for all k≥kmin≈kc. Our results provide a novel way to determine kc in SYK-type models.

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Phys. Rev. D 112, 046017– Published 21 August, 2025
  • Received 18 August 2024
  • Accepted 30 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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