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arXiv · 1812.02666

On the replica structure of Sachdev-Ye-Kitaev model

Hanteng Wang·D. Bagrets·A. L. Chudnovskiy·A. Kamenev
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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.

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Hanteng Wang, D. Bagrets, A. L. Chudnovskiy, A. Kamenev. 2018-12-06. On the replica structure of Sachdev-Ye-Kitaev model. https://doi.org/10.1007/jhep09(2019)057

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