Deformed Dolan-Grady relations in quantum integrable models
Deformed Dolan-Grady relations in quantum integrable models
复制标题
量子可积模型中变形的 Dolan-Grady 关系
DOI：
10.1016/j.nuclphysb.2004.12.016
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
P. Baseilhac
中科院分区：
文献类型：
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作者：
P. Baseilhac
在反射方程和相关的量子可积模型中发现了一种新的隐对称性。它是由符合q-变形Dolan-Grady关系的一对算子{a， a∗}∈a生成的。利用逆散射方法，提出了一种新的量子可积模型族。在最简单的情况下，哈密顿量在a的基本生成子中是线性的。对于q的一般值，相应的谱问题是准精确可解的。在此基础上，重新考虑了二维质量/无质量（边界）可积模型的几个例子，明确地构造了A的基本生成器，并得到了精确的结果。特别地，我们在（边界）sin - gordon模型中展示了一个动态Askey-Wilson对称代数，并证明了渐近（边界）状态可以用q正交多项式表示。
A new hidden symmetry is exhibited in the reflection equation and related quantum integrable models. It is generated by a dual pair of operators {A,A∗}∈A subject to q-deformed Dolan–Grady relations. Using the inverse scattering method, a new family of quantum integrable models is proposed. In the simplest case, the Hamiltonian is linear in the fundamental generators of A. For general values of q, the corresponding spectral problem is quasi-exactly solvable. Several examples of two-dimensional massive/massless (boundary) integrable models are reconsidered in light of this approach, for which the fundamental generators of A are constructed explicitly and exact results are obtained. In particular, we exhibit a dynamical Askey–Wilson symmetry algebra in the (boundary) sine-Gordon model and show that asymptotic (boundary) states can be expressed in terms of q-orthogonal polynomials.