A new (in)finite-dimensional algebra for quantum integrable models
A new (in)finite-dimensional algebra for quantum integrable models
复制标题
量子可积模型的新（内）有限维代数
DOI：
10.1016/j.nuclphysb.2005.05.021
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
K. Koizumi
中科院分区：
文献类型：
--
作者：
P. Baseilhac;K. Koizumi
引入了一个新的（非）有限维代数，它是一大类（连续或格）量子可积模型的基本动力学对称性。三维表示构造和相互交换的数量-这确保了系统的可积性-写在新代数的基本发电机。描述了作者之一最近发现的变形Dolan-Grady可积结构与Terwilliger三对角代数的关系。值得注意的是，这个（在）有限维代数是一个“q变形”的模拟原始昂萨格的代数中产生的平面伊辛模型。因此，它提供了一个新的和替代的代数框架，研究大量的，以及共形，量子可积模型。
A new (in)finite-dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite-dimensional representations are constructed and mutually commuting quantities—which ensure the integrability of the system—are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan–Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite-dimensional algebra is a “q-deformed” analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models.