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

Abstract

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.

References in corpus (3)

• The open XXX spin chain in the SoV framework: scalar product of separate states
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• The Kowalewski's top revisited