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Title: 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:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  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)
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.
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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
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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.
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@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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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1007/jhep11(2023)088
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