Gu, Yingfei and Kitaev, Alexei and Zhang, Pengfei (2022) A two-way approach to out-of-time-order correlators. Journal of High Energy Physics, 2022 (3). Art. No. 133. ISSN 1029-8479. doi:10.1007/jhep03(2022)133. https://resolver.caltech.edu/CaltechAUTHORS:20220323-545297000
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Abstract
Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-N systems such as the SYK model, is to replace the actual source with some mean-field perturbation and solve for the probe correlation function on the double Keldysh contour. We show how to obtain the OTOC by combining two such solutions for perturbations propagating forward and backward in time. These dynamical perturbations, or scrambling modes, are considered on the thermofield double background and decomposed into a coherent and an incoherent part. For the large-q SYK, we obtain the OTOC in a closed form. We also prove a previously conjectured relation between the Lyapunov exponent and high-frequency behavior of the spectral function.
| Item Type: | Article | ||||||||||||
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| Additional Information: | © 2022 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received 01 December 2021. Accepted 01 March 2022. Published 21 March 2022. We thank Douglas Stanford and Juan Maldacena for useful comments. Yingfei Gu and Pengfei Zhang also thank Shunyu Yao for explaining the paper [22] to them. Yingfei Gu is supported by the Simons Foundation through the “It from Qubit” program. Alexei Kitaev is supported by the Simons Foundation under grant 376205 and through the “It from Qubit” program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. Pengfei Zhang acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech. | ||||||||||||
| Group: | Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics | ||||||||||||
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| Subject Keywords: | 1/N Expansion; Field Theories in Lower Dimensions; AdS-CFT Correspondence | ||||||||||||
| Issue or Number: | 3 | ||||||||||||
| DOI: | 10.1007/jhep03(2022)133 | ||||||||||||
| Record Number: | CaltechAUTHORS:20220323-545297000 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20220323-545297000 | ||||||||||||
| Official Citation: | Gu, Y., Kitaev, A. & Zhang, P. A two-way approach to out-of-time-order correlators. J. High Energ. Phys. 2022, 133 (2022). https://doi.org/10.1007/JHEP03(2022)133 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 114017 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | George Porter | ||||||||||||
| Deposited On: | 23 Mar 2022 20:23 | ||||||||||||
| Last Modified: | 06 Dec 2022 18:48 |
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