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New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 matrices the constructed separated variables can be directly identified with action-angle coordinates.
Keywords: integrable spin chains, quadratic Sklyanin brackets, separation of variables. 
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     author = {Guido Magnano and Taras Skrypnyk},
     title = {New {Separation} of {Variables} for the {Classical} {XXX} and {XXZ} {Heisenberg} {Spin} {Chains}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a46/}
}
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Guido Magnano; Taras Skrypnyk. New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a46/

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