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

Avijit Das, Saurish Chakrabarty, Abhishek Dhar, Anupam Kundu, David A. Huse, Roderich Moessner, Samriddhi Sankar Ray, Subhro Bhattacharjee

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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.

Original languageEnglish (US)
Article number024101
JournalPhysical review letters
Volume121
Issue number2
DOIs
StatePublished - Jul 10 2018

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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    Das, A., Chakrabarty, S., Dhar, A., Kundu, A., Huse, D. A., Moessner, R., Ray, S. S., & Bhattacharjee, S. (2018). Light-Cone Spreading of Perturbations and the Butterfly Effect in a Classical Spin Chain. Physical review letters, 121(2), [024101]. https://doi.org/10.1103/PhysRevLett.121.024101