Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories
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PhysRevLett.117.091602.pdf
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132.24 KB
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Author(s)
Roberts, Daniel Adam
Swingle, Brian Gordon
Date Issued
August 2016
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Roberts, Daniel A., and Brian Swingle. “Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories.” Physical Review Letters 117.9 (2016): n. pag. © 2016 American Physical Society
Version
Final published version
Abstract
As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one such bound—the Lieb-Robinson bound—and the butterfly effect in strongly coupled quantum systems. The butterfly effect implies the ballistic growth of local operators in time, which can be quantified with the “butterfly” velocity v_{B}. Similarly, the Lieb-Robinson velocity places a state-independent ballistic upper bound on the size of time evolved operators in nonrelativistic lattice models. Here, we argue that v_{B} is a state-dependent effective Lieb-Robinson velocity. We study the butterfly velocity in a wide variety of quantum field theories using holography and compare with free-particle computations to understand the role of strong coupling. We find that v_{B} remains constant or decreases with decreasing temperature. We also comment on experimental prospects and on the relationship between the butterfly velocity and signaling.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.117.091602
