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Out-of-time-ordered correlators in many-body localized systems

Huang, Yichen and Zhang, Yong-Liang and Chen, Xie (2017) Out-of-time-ordered correlators in many-body localized systems. Annalen der Physik, 529 (7). Art. No. 1600318. ISSN 0003-3804. http://resolver.caltech.edu/CaltechAUTHORS:20161114-153129646

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Abstract

In many-body localized systems, propagation of information forms a light cone that grows logarithmically with time. However, local changes in energy or other conserved quantities typically spread only within a finite distance. Is it possible to detect the logarithmic light cone generated by a local perturbation from the response of a local operator at a later time? We numerically calculate various correlators in the random-field Heisenberg chain. While the equilibrium retarded correlator A(t = 0)B(t > 0) is not sensitive to the unbounded information propagation, the out-of-time-ordered correlator A(t = 0)B(t > 0)A(t = 0)B(t > 0) can detect the logarithmic light cone. We relate out-of-time-ordered correlators to the Lieb-Robinson bound in many-body localized systems, and show how to detect the logarithmic light cone with retarded correlators in specially designed states. Furthermore, we study the temperature dependence of the logarithmic light cone using out-of-time-ordered correlators.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/andp.201600318DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/andp.201600318/abstractPublisherArticle
https://arxiv.org/abs/1608.01091arXivDiscussion Paper
Alternate Title:Out-of-Time-Ordered Correlator in Many-Body Localized Systems
Additional Information:© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. Issue online: 5 July 2017; Version of record online: 9 December 2016; Manuscript Revised: 17 November 2016; Manuscript Accepted: 17 November 2016; Manuscript Received: 18 October 2016. We would like to thank Yoni BenTov, Manuel Endres, Alexei Y. Kitaev, Joel E. Moore, and Rahul Nandkishore for inspiring discussions. In particular, we would like to acknowledge discussions with Yingfei Gu, which led to the study of the temperature dependence of logarithmic light cones. Y.H. and X.C. acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-2644). X.C. is also supported by the Walter Burke Institute for Theoretical Physics.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20161114-153129646
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161114-153129646
Official Citation:Y. Huang, Y. Zhang, X. Chen, ANNALEN DER PHYSIK 2017, 529, . https://doi.org/10.1002/andp.201600318
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72003
Collection:CaltechAUTHORS
Deposited By: Melissa Ray
Deposited On:15 Nov 2016 21:46
Last Modified:26 Jul 2017 22:25

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