论文标题
可集成的Q形式的各向异性Haldane-Shastry长距离旋转链的椭圆概括
Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
论文作者
论文摘要
我们描述了可集成的椭圆形的Q-脱离各向异性的远程旋转链。该推导基于我们最近的通勤椭圆形旋转Ruijsenaars-Macdonald操作员的建筑。我们证明可以将多chranakos冻结技巧应用于这些操作员，从而为远程旋转链提供了通勤的汉密尔顿人，该链条通过椭圆形的baxter baxter-belavin $ {\ rm gl} _m $ $ $ $ $ $ $ r $ r $ -matrix。也就是说，我们证明了冻结技巧被简化为一组椭圆函数身份，然后证明了这些函数。这些身份可以视为在基本的无旋转Ruijsenaars-Schneider模型中平衡位置的条件。也研究了三角变性。例如，在$ m = 2 $案例中，我们的构造为各向异性xxz haldane-shastry型号提供了q信息。标准的Haldane-Shastry模型及其基于$ {\ rm U} _Q（{\ wideHat {\ rm gl} _m}）$ xxz $ r $ -matrix的Q-efformation被单独验证包括在内。
We describe integrable elliptic q-deformed anisotropic long-range spin chain. The derivation is based on our recent construction for commuting anisotropic elliptic spin Ruijsenaars-Macdonald operators. We prove that the Polychronakos freezing trick can be applied to these operators, thus providing the commuting set of Hamiltonians for long-range spin chain constructed by means of the elliptic Baxter-Belavin ${\rm GL}_M$ $R$-matrix. Namely, we show that the freezing trick is reduced to a set of elliptic function identities, which are then proved. These identities can be treated as conditions for equilibrium position in the underlying classical spinless Ruijsenaars-Schneider model. Trigonometric degenerations are studied as well. For example, in $M=2$ case our construction provides q-deformation for anisotropic XXZ Haldane-Shastry model. The standard Haldane-Shastry model and its Uglov's q-deformation based on ${\rm U}_q({\widehat {\rm gl}_M})$ XXZ $R$-matrix are included into consideration by separate verification.
