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Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories

Daniel A. Roberts and Brian Swingle
Phys. Rev. Lett. 117, 091602 – Published 23 August 2016
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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 vB. 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 vB 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 vB remains constant or decreases with decreasing temperature. We also comment on experimental prospects and on the relationship between the butterfly velocity and signaling.

  • Received 25 May 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.091602

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsGravitation, Cosmology & AstrophysicsQuantum Information, Science & TechnologyStatistical Physics & Thermodynamics

Authors & Affiliations

Daniel A. Roberts*

  • Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Brian Swingle

  • Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305, USA

  • *drob@mit.edu
  • bswingle@stanford.edu

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Issue

Vol. 117, Iss. 9 — 26 August 2016

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