New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains

@article{Magnano2020NewSO,
  title={New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains},
  author={Guido Magnano and T. Skrypnyk},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2020},
  pages={1-27}
}
  • G. Magnano, T. Skrypnyk
  • Published 2 June 2020
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
We propose a non-standard separation of variables for the classical integrable XXX and XXZ spin chains with degenerate twist matrix. We show that for the case of such twist matrices one can interchange the role of classical separating functions $A(u)$ and $B(u)$ and construct a new full set of separated variables, satisfying simpler equation of separation and simpler Abel equations in comparison with the standard separated variables of Sklyanin. We show that for certain cases of the twist… 
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