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Title: On the replica structure of Sachdev-Ye-Kitaev model

Abstract

We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the soft-mode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and replica-off-diagonal calculations. We conclude that all our numerical results are in a quantitative agreement with the theory based on the replica-diagonal saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do contain replica off-diagonal components). This seems to exclude any contributions from replica-off-diagonal saddle points, at least on the time scales shorter than the inverse many-body level spacing.

Authors:
 [1];  [2]; ORCiD logo [3];  [1]
  1. Univ. of Minnesota, Minneapolis, MN (United States)
  2. Universität zu Köln (Germany)
  3. Univ. of Hamburg (Germany)
Publication Date:
Research Org.:
Yale Univ., New Haven, CT (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1609975
Grant/Contract Number:  
FG02-08ER46482; DMR-1608238
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2019; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Random Systems; Field Theories in Lower Dimensions; Holography and condensed matter physics (AdS/CMT)

Citation Formats

Wang, Hanteng, Bagrets, D., Chudnovskiy, A. L., and Kamenev, A. On the replica structure of Sachdev-Ye-Kitaev model. United States: N. p., 2019. Web. doi:10.1007/jhep09(2019)057.
Wang, Hanteng, Bagrets, D., Chudnovskiy, A. L., & Kamenev, A. On the replica structure of Sachdev-Ye-Kitaev model. United States. https://doi.org/10.1007/jhep09(2019)057
Wang, Hanteng, Bagrets, D., Chudnovskiy, A. L., and Kamenev, A. Mon . "On the replica structure of Sachdev-Ye-Kitaev model". United States. https://doi.org/10.1007/jhep09(2019)057. https://www.osti.gov/servlets/purl/1609975.
@article{osti_1609975,
title = {On the replica structure of Sachdev-Ye-Kitaev model},
author = {Wang, Hanteng and Bagrets, D. and Chudnovskiy, A. L. and Kamenev, A.},
abstractNote = {We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the soft-mode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and replica-off-diagonal calculations. We conclude that all our numerical results are in a quantitative agreement with the theory based on the replica-diagonal saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do contain replica off-diagonal components). This seems to exclude any contributions from replica-off-diagonal saddle points, at least on the time scales shorter than the inverse many-body level spacing.},
doi = {10.1007/jhep09(2019)057},
url = {https://www.osti.gov/biblio/1609975}, journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 9,
volume = 2019,
place = {United States},
year = {2019},
month = {9}
}

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Cited by: 4 works
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Works referenced in this record:

Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid
journal, December 2018


Sachdev–Ye–Kitaev model as Liouville quantum mechanics
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journal, November 2017


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A generalization of Sachdev-Ye-Kitaev
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    Works referencing / citing this record:

    Revealing Nonperturbative Effects in the SYK Model
    journal, November 2019