Elliptic generalisation of integrable q-deformed anisotropic Haldane–Shastry long-range spin chain

We describe integrable elliptic q-deformed anisotropic long-range spin chain. The derivation is based on our recent construction for commuting Ruijsenaars-Macdonald operators. prove that the Polychronakos freezing trick can be applied to these operators, thus providing set of Hamiltonians chain constructed by means Baxter-Belavin ${\rm GL}_M$ $R$-matrix. Namely, we show reduced a function identities, which are then proved. These identities treated as conditions equilibrium position in underlying classical spinless Ruijsenaars-Schneider model. Trigonometric degenerations studied well. For example, $M=2$ case provides q-deformation XXZ Haldane-Shastry standard model and its Uglov's U}_q({\widehat {\rm gl}_M})$ $R$-matrix included into consideration separate verification.