Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories
Author(s)
Roberts, Daniel Adam; Swingle, Brian Gordon
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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.
Date issued
2016-08Department
Massachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of PhysicsJournal
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
ISSN
0031-9007
1079-7114