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Light-Cone Spreading of Perturbations and the Butterfly Effect in a Classical Spin Chain

Author(s): Das, Avijit; Chakrabarty, Saurish; Dhar, Abhishek; Kundu, Anupam; Huse, David A; et al

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Abstract: We find that the effects of a localized perturbation in a chaotic classical many-body system-the classical Heisenberg chain at infinite temperature-spread ballistically with a finite speed even when the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterized by the Lyapunov exponents and the butterfly speed, respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a natural correlator in our system and demonstrate that many of its interesting qualitative features are present in the classical system. Finally, by analyzing the scaling forms, we relate the growth, spread, and propagation of the perturbation with the growth of one-dimensional interfaces described by the Kardar-Parisi-Zhang equation.
Publication Date: 10-Jul-2018
Electronic Publication Date: 13-Jul-2018
Citation: Das, Avijit, Chakrabarty, Saurish, Dhar, Abhishek, Kundu, Anupam, Huse, David A, Moessner, Roderich, Ray, Samriddhi Sankar, Bhattacharjee, Subhro. (2018). Light-Cone Spreading of Perturbations and the Butterfly Effect in a Classical Spin Chain. PHYSICAL REVIEW LETTERS, 121 (10.1103/PhysRevLett.121.024101
DOI: doi:10.1103/PhysRevLett.121.024101
ISSN: 0031-9007
EISSN: 1079-7114
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW LETTERS
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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