Sparsity dependence of Krylov state complexity in the SYK model

Jha, Raghav G.; Roy, Ranadeep

doi:10.1103/qsyk-m3sg

Sparsity dependence of Krylov state complexity in the SYK model

Journal Article · Thu Aug 21 00:00:00 EDT 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/qsyk-m3sg· OSTI ID:2584657

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Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
The Ohio State Univ., Columbus, OH (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-06OR23177; SC0012704

OSTI ID:: 2584657

Report Number(s):: DOE/OR/23177-7578; JLAB-THY--24-4131; arXiv:2407.20569

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 4 Vol. 112; ISSN 2470-0010; ISSN 2470-0029

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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