Interacting finite-size magnons

Klose, Thomas; McLoughlin, Tristan

doi:10.1088/1751-8113/41/28/285401

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Interacting finite-size magnons

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McLoughlin, Tristan
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Klose, T., & McLoughlin, T. (2008). Interacting finite-size magnons. Journal of Physics A: Mathematical and Theoretical, 41(28): 285401. doi:10.1088/1751-8113/41/28/285401.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-6334-1

Abstract

We explicitly construct a large class of finite-volume two-magnon string solutions moving on R x S^2. In particular, by making use of the relationship between the O(3) sigma model and sine-Gordon theory we are able to find solutions corresponding to the periodic analogues of magnon scattering and breather-like solutions. After semi-classically quantizing these solutions we invert the implicit expressions for the excitation energies in certain limits and find the corrections for the multi-magnon states. For the breather-like solutions we express the energies directly in terms of the action variable whereas for the scattering solution we express the result as a combination of corrections to the dispersion relation and to the scattering phase.