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arXiv:1506.01554 · Journal of Statistical Mechanics Theory and Experiment

Three magnons in an isotropic S = 1 ferromagnetic chain as an exactly solvable non-integrable system

P N Bibikov

Published Mar 1, 2016• 7 citations
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Abstract

Abstract It is shown that a generalization of the Bethe ansatz based on a utilization of degenerative discrete-diffractive wave functions solves the three-magnon problem for the S = 1 isotropic ferromagnetic infinite chain. The four-magnon problem is briefly discussed.
DOI
10.1088/1742-5468/2016/03/033109

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Abstract Two different versions of Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg–Ising ferromagnets on square and simple cubic lattices. It is shown that the two-magnon sector is subdivided on two subsectors related to non-interacting and scattering magnons. The former subsector possess an integrable regular dynamics and may be described by a natural modification of the usual Bethe Ansatz. The latter one is characterized by a non-integrable chaotic dynamics and may be treated only within discrete degenerative version of Bethe Ansatz previously suggested by the author. Some of these results are generalized for multi-magnon states of the Heisenberg–Ising ferromagnet on a D dimensional hyper cubic lattice.
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