Out-of-time-ordered correlators in many-body localized systems
- Creators
- Huang, Yichen
- Zhang, Yong-Liang
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Chen, Xie
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.
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.Attached Files
Submitted - 1608.01091v2.pdf
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Additional details
- Alternative title
- Out-of-Time-Ordered Correlator in Many-Body Localized Systems
- Eprint ID
- 72003
- Resolver ID
- CaltechAUTHORS:20161114-153129646
- Institute for Quantum Information and Matter (IQIM)
- NSF
- PHY-1125565
- Gordon and Betty Moore Foundation
- GBMF-2644
- Walter Burke Institute for Theoretical Physics, Caltech
- Created
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2016-11-15Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics