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Finite-size scaling of out-of-time-ordered correlators at late times

Huang, Yichen and Brandão, Fernando G. S. L. and Zhang, Yong-Liang (2019) Finite-size scaling of out-of-time-ordered correlators at late times. Physical Review Letters, 123 (1). Art. No. 010601. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20170726-091047115

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Abstract

Chaotic dynamics in quantum many-body systems scrambles local information so that at late times it can no longer be accessed locally. This is reflected quantitatively in the out-of-time-ordered correlator of local operators, which is expected to decay to 0 with time. However, for systems of finite size, out-of-time-ordered correlators do not decay exactly to 0 and in this paper we show that the residual value can provide useful insights into the chaotic dynamics. When energy is conserved, the late-time saturation value of the out-of-time-ordered correlator of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We provide both analytical arguments and numerical simulations to support this conclusion.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.123.010601DOIArticle
https://arxiv.org/abs/1705.07597arXivDiscussion Paper
ORCID:
AuthorORCID
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2019 American Physical Society. Received 2 January 2018; revised manuscript received 11 May 2018; published 1 July 2019. We thank Xie Chen, Yingfei Gu, Nick Hunter-Jones, Alexei Y. Kitaev, and Douglas Stanford for helpful discussions. We are especially grateful to X. C., who wrote a substantial portion of this Letter. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant No. PHY-1733907). Additional funding support was provided by NSF Grant No. DMR-1654340 (Y. H. and Y.-L. Z.).
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1733907
NSFDMR-1654340
Record Number:CaltechAUTHORS:20170726-091047115
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170726-091047115
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79397
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Jul 2017 16:18
Last Modified:08 Jul 2019 18:14

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