Symmetries and exact solutions of some integrable Haldane-Shastry-like spin chains Original Research Article

Here we construct some integrable Haldane-Shastry (HS) like spin chains, which exhibit multi-parameter deformed or non-standard variants of Y(glm) Yangian symmetry. By projecting the eigenstates of Dunkl operators in a suitable way, we also derive a class of exact eigenfunctions for such spin chains and subsequently conjecture that these exact eigenfunctions would lead to the highest weight states (HWS) associated with multi-parameter deformed or non-standard variants of Y(glM) Yangian algebra. By using this conjecture, and acting descendent operator on the HWS associated with a non-standard Y(gl2) Yangian algebra, we are able to find out the complete set of eigenvalues and eigenfunctions for the related HS-like spin-12 chain. It turns out that some additional energy levels, which are forbidden due to a selection rule in the case of SU(2) HS model, interestingly appear in the spectrum of the above mentioned HS-like spin chain with non-standard Y(gl2) symmetry.