Published February 2019
| Submitted + Published
Journal Article
Open
On the relation between the magnitude and exponent of OTOCs
- Creators
-
Gu, Yingfei
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Kitaev, Alexei
Chicago
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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.
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.Attached Files
Published - Gu-Kitaev2019_Article_OnTheRelationBetweenTheMagnitu.pdf
Submitted - 1812.00120.pdf
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Additional details
- Eprint ID
- 92991
- Resolver ID
- CaltechAUTHORS:20190220-075207560
- Gordon and Betty Moore Foundation
- GBMF-4306
- Simons Foundation
- 376205
- It from Qubit Program
- Institute of Quantum Information and Matter (IQIM)
- NSF
- PHY-1607611
- NSF
- PHY-1748958
- SCOAP3
- Created
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2019-02-20Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter