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

Abstract

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 .

22 pages + 18 pages Appendices, 13 Figures. Version submitted to JHEP for publication

References in corpus (3)

• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Binary-coupling sparse SYK: an improved model of quantum chaos and holography
• Quantum chaos in a weakly-coupled field theory with nonlocality

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