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.
Original language | English (US) |
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Article number | 57 |
Journal | Journal of High Energy Physics |
Volume | 2019 |
Issue number | 9 |
DOIs | |
State | Published - Sep 1 2019 |
Bibliographical note
Publisher Copyright:© 2019, The Author(s).
Keywords
- Field Theories in Lower Dimensions
- Holography and condensed matter physics (AdS/CMT)
- Random Systems