XXZ模型及其对称代数的结构

XXZ Model and the Structure of the Symmetric Algebra

本文以具量子代数SL_q(2)对称性的XXZ Heisenberg自旋链为例,利用Temperley-Lieb代数结构,深入分析q^p=±1时SL_q(2)量子代数的有限维表示,讨论了可约而不可分解表示(Ⅰ型表示)出现的条件及其性质,并采用取极限办法得到新的状态,从而得到对应确定能量状态的完全集合。

In this paper, an XXZ model of the Heisenberg spin chain with the symmetry of the quantum SL_q(2) enveloping algebra is discussed. In terms of the structure of the Temperley-Lieb algebra, in this model we analyse the finite-dimensional representations of the quantum SL_q(2) with q^p=±1 in some detail, including the condition of appearance of the reducible but indecomposable representations (type Ⅰ representation), their properties, and the completeset of the states related to a definite energy where the new states are obtained by an appropriare limit process.