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

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.
Authors:
 [1] ;  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics and Dept. of Physics
  2. Stanford Univ., CA (United States). Inst. for Theoretical Physics and Dept. of Physics
Publication Date:
Grant/Contract Number:
SC0012567
Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 117; Journal Issue: 9; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Research Org:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; 79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
1505740
Alternate Identifier(s):
OSTI ID: 1328616

Roberts, Daniel A., and Swingle, Brian. Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories. United States: N. p., Web. doi:10.1103/physrevlett.117.091602.
Roberts, Daniel A., & Swingle, Brian. Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories. United States. doi:10.1103/physrevlett.117.091602.
Roberts, Daniel A., and Swingle, Brian. 2016. "Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories". United States. doi:10.1103/physrevlett.117.091602. https://www.osti.gov/servlets/purl/1505740.
@article{osti_1505740,
title = {Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories},
author = {Roberts, Daniel A. and Swingle, Brian},
abstractNote = {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 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.},
doi = {10.1103/physrevlett.117.091602},
journal = {Physical Review Letters},
number = 9,
volume = 117,
place = {United States},
year = {2016},
month = {8}
}