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Rogue breather modes: Topological sectors, and the ‘belt-trick’, in a one-dimensional ferromagnetic spin chain

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  • Rahul, O.R.
  • Murugesh, S.

Abstract

We present explicit solutions for breather soliton modes of excitation in the one-dimensional Heisenberg ferromagnetic spin chain. We identify a characteristic geometrical feature of these breather modes wherein a helicoidal configuration of spins is continuously transformed to one which differs from the initial helicoid by a total twist of ‘2’. This is a curious manoeuvre popularly known as the ‘belt trick’, an illustration of the simple connectedness of the SU(2) group manifold, and its rotation period 4π. We show that this effectively splits the configuration space of the ferromagnetic chain in one-dimension into two topological sectors, distinguished by their total twist — either ‘0’, or ‘1’. Further, the energy lower bound of the two sectors is separated by a finite gap varying inversely with the size of the lattice.

Suggested Citation

  • Rahul, O.R. & Murugesh, S., 2019. "Rogue breather modes: Topological sectors, and the ‘belt-trick’, in a one-dimensional ferromagnetic spin chain," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 262-269.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:262-269
    DOI: 10.1016/j.chaos.2019.02.012
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    References listed on IDEAS

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    1. L. Faddeev & Antti J. Niemi, 1997. "Stable knot-like structures in classical field theory," Nature, Nature, vol. 387(6628), pages 58-61, May.
    2. Aritra K. Mukhopadhyay & Vivek M. Vyas & Prasanta K. Panigrahi, 2015. "Rogue waves and breathers in Heisenberg spin chain," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(7), pages 1-5, July.
    3. Lakshmanan, M. & Ruijgrok, Th.W. & Thompson, C.J., 1976. "On the dynamics of a continuum spin system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 577-590.
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