Sparsity dependence of Krylov state complexity in the SYK model - Jha, Raghav G.; Roy, Ranadeep (Physical review. D, 2025)
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 k c , 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 ≥ k min 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 ≥ k min ≈ k c . Our results provide a novel way to determine k c in SYK-type models.