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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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dc.contributor.authorDas, Avijit-
dc.contributor.authorChakrabarty, Saurish-
dc.contributor.authorDhar, Abhishek-
dc.contributor.authorKundu, Anupam-
dc.contributor.authorHuse, David A-
dc.contributor.authorMoessner, Roderich-
dc.contributor.authorRay, Samriddhi Sankar-
dc.contributor.authorBhattacharjee, Subhro-
dc.date.accessioned2022-01-25T15:03:05Z-
dc.date.available2022-01-25T15:03:05Z-
dc.date.issued2018-07-10en_US
dc.identifier.citationDas, 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.121.024101en_US
dc.identifier.issn0031-9007-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1n00zt0d-
dc.description.abstractWe 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.en_US
dc.language.isoen_USen_US
dc.relation.ispartofPHYSICAL REVIEW LETTERSen_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleLight-Cone Spreading of Perturbations and the Butterfly Effect in a Classical Spin Chainen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1103/PhysRevLett.121.024101-
dc.date.eissued2018-07-13en_US
dc.identifier.eissn1079-7114-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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