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On the relation between the magnitude and exponent of OTOCs

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. http://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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/JHEP02(2019)075DOIArticle
https://arxiv.org/abs/1812.00120arXivDiscussion Paper
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:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Gordon and Betty Moore FoundationGBMF-4306
Simons Foundation376205
It from Qubit ProgramUNSPECIFIED
Institute of Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1607611
NSFPHY-1748958
SCOAP3UNSPECIFIED
Subject Keywords:AdS-CFT Correspondence; 1/N Expansion; Models of Quantum Gravity
Record Number:CaltechAUTHORS:20190220-075207560
Persistent URL:http://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:20 Feb 2019 16:01

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