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Title: Quantum scrambling and state dependence of the butterfly velocity

Abstract

Operator growth in spatially local quantum many-body systems defines a scrambling velocity. We prove that this scrambling velocity bounds the state dependence of the out-of-time-ordered correlator in local lattice models. We verify this bound in simulations of the thermal mixed-field Ising spin chain. For scrambling operators, the butterfly velocity shows a crossover from a microscopic high temperature value to a distinct value at temperatures below the energy gap.

Authors:
 [1];  [1]
  1. Stanford University
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1569772
Grant/Contract Number:  
SC0018134
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 7 Journal Issue: 4; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Han, Xizhi, and Hartnoll, Sean. Quantum scrambling and state dependence of the butterfly velocity. Netherlands: N. p., 2019. Web. doi:10.21468/SciPostPhys.7.4.045.
Han, Xizhi, & Hartnoll, Sean. Quantum scrambling and state dependence of the butterfly velocity. Netherlands. doi:10.21468/SciPostPhys.7.4.045.
Han, Xizhi, and Hartnoll, Sean. Tue . "Quantum scrambling and state dependence of the butterfly velocity". Netherlands. doi:10.21468/SciPostPhys.7.4.045.
@article{osti_1569772,
title = {Quantum scrambling and state dependence of the butterfly velocity},
author = {Han, Xizhi and Hartnoll, Sean},
abstractNote = {Operator growth in spatially local quantum many-body systems defines a scrambling velocity. We prove that this scrambling velocity bounds the state dependence of the out-of-time-ordered correlator in local lattice models. We verify this bound in simulations of the thermal mixed-field Ising spin chain. For scrambling operators, the butterfly velocity shows a crossover from a microscopic high temperature value to a distinct value at temperatures below the energy gap.},
doi = {10.21468/SciPostPhys.7.4.045},
journal = {SciPost Physics Proceedings},
number = 4,
volume = 7,
place = {Netherlands},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.7.4.045

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