Out-of-time-order correlators and Lyapunov exponents in sparse SYK

Journal Article · 15 November 2023 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep11(2023)088 · OSTI ID:2212864

Cáceres, Elena  ^[1]; Guglielmo, Tyler  ^[2]; Kent, Brian  ^[1]; Misobuchi, Anderson  ^[1]

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1. Univ. of Texas, Austin, TX (United States)
2. Univ. of Texas, Austin, TX (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order of N, the standard result for the q-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter, k. We present an algorithm to sum the diagrams at any given order of 1/(kq)ⁿ. We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finite N becomes more significant for larger values of N.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 2212864
• Report Number(s): LLNL--JRNL-849296; 1074904
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 11 Vol. 2023; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English