Gu, Yingfei and Kitaev, Alexei (2019) On the relation between the magnitude and exponent of OTOCs. Journal of High Energy Physics, 2019 (2). Art. No. 75. ISSN 1126-6708. doi:10.1007/JHEP02(2019)075. https://resolver.caltech.edu/CaltechAUTHORS:20190220-075207560
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Abstract
We derive an identity relating the growth exponent of early-time OTOCs, the pre-exponential factor, and a third number called “branching time”. The latter is defined within the dynamical mean-field framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models; we also explicitly define “strings” in this context. As another application, we consider an SYK chain. If the coupling strength βJ is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly 2π/β.
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| Additional Information: | © 2019 The Author(s). 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: January 15, 2019; Accepted: February 8, 2019; Published: February 13, 2019. We thank David Huse, Juan Maldacena, Xiao-Liang Qi, Subir Sachdev, Steve Shenker, Douglas Stanford, Josephine Suh and Ashvin Vishwanath for useful discussions. Y.G. is supported by the Gordon and Betty Moore Foundation EPiQS Initiative through Grant (GBMF-4306). A.K. 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. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611, and at KITP, supported by the NSF grant PHY-1748958. | ||||||||||||||||
| Group: | Institute for Quantum Information and Matter | ||||||||||||||||
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| Subject Keywords: | AdS-CFT Correspondence; 1/N Expansion; Models of Quantum Gravity | ||||||||||||||||
| Issue or Number: | 2 | ||||||||||||||||
| DOI: | 10.1007/JHEP02(2019)075 | ||||||||||||||||
| Record Number: | CaltechAUTHORS:20190220-075207560 | ||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190220-075207560 | ||||||||||||||||
| Official Citation: | Gu, Y. & Kitaev, A. J. High Energ. Phys. (2019) 2019: 75. https://doi.org/10.1007/JHEP02(2019)075 | ||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||
| ID Code: | 92991 | ||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||||||
| Deposited On: | 20 Feb 2019 16:01 | ||||||||||||||||
| Last Modified: | 16 Nov 2021 16:55 |
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