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 .
Keywords
Cite
@article{arxiv.2306.07345,
title = {Out-of-time-order correlators and Lyapunov exponents in sparse SYK},
author = {Elena Cáceres and Tyler Guglielmo and Brian Kent and Anderson Misobuchi},
journal= {arXiv preprint arXiv:2306.07345},
year = {2023}
}
Comments
22 pages + 18 pages Appendices, 13 Figures. Version submitted to JHEP for publication