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.
- Authors:
-
- Univ. of Texas, Austin, TX (United States)
- Univ. of Texas, Austin, TX (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 2212864
- Report Number(s):
- LLNL-JRNL-849296
Journal ID: ISSN 1029-8479; 1074904
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2023; Journal Issue: 11; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 2D gravity; AdS-CFT correspondence; Holography and Condensed Matter Physics (AdS/CMT); Random systems
Citation Formats
Cáceres, Elena, Guglielmo, Tyler, Kent, Brian, and Misobuchi, Anderson. Out-of-time-order correlators and Lyapunov exponents in sparse SYK. United States: N. p., 2023.
Web. doi:10.1007/jhep11(2023)088.
Cáceres, Elena, Guglielmo, Tyler, Kent, Brian, & Misobuchi, Anderson. Out-of-time-order correlators and Lyapunov exponents in sparse SYK. United States. https://doi.org/10.1007/jhep11(2023)088
Cáceres, Elena, Guglielmo, Tyler, Kent, Brian, and Misobuchi, Anderson. Thu .
"Out-of-time-order correlators and Lyapunov exponents in sparse SYK". United States. https://doi.org/10.1007/jhep11(2023)088. https://www.osti.gov/servlets/purl/2212864.
@article{osti_2212864,
title = {Out-of-time-order correlators and Lyapunov exponents in sparse SYK},
author = {Cáceres, Elena and Guglielmo, Tyler and Kent, Brian and Misobuchi, Anderson},
abstractNote = {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.},
doi = {10.1007/jhep11(2023)088},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2023,
place = {United States},
year = {Thu Nov 16 00:00:00 EST 2023},
month = {Thu Nov 16 00:00:00 EST 2023}
}
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