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  • Letter
  • Open Access

Long-lived solitons and their signatures in the classical Heisenberg chain

Adam J. McRoberts1, Thomas Bilitewski1,2, Masudul Haque1,3,4, and Roderich Moessner1

  • 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
  • 2Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA
  • 3Department of Theoretical Physics, Maynooth University, County Kildare, Ireland
  • 4Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany

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Phys. Rev. E 106, L062202 – Published 16 December, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.L062202

Abstract

Motivated by the Kardar-Parisi-Zhang (KPZ) scaling recently observed in the classical ferromagnetic Heisenberg chain, we investigate the role of solitonic excitations in this model. We find that the Heisenberg chain, although well known to be nonintegrable, supports a two-parameter family of long-lived solitons. We connect these to the exact soliton solutions of the integrable Ishimori chain with ln(1+Si·Sj) interactions. We explicitly construct infinitely long-lived stationary solitons, and provide an adiabatic construction procedure for moving soliton solutions, which shows that Ishimori solitons have a long-lived Heisenberg counterpart when they are not too narrow and not too fast moving. Finally, we demonstrate their presence in thermal states of the Heisenberg chain, even when the typical soliton width is larger than the spin correlation length, and argue that these excitations likely underlie the KPZ scaling.

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Outline

Information

Phys. Rev. E 106, L062202– Published 16 December, 2022
  • Received 4 August 2022
  • Accepted 28 November 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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