Onsager symmetries in $U(1)$ -invariant clock models
Onsager symmetries in $U(1)$ -invariant clock models
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$U(1)$ 不变时钟模型中的 Onsager 对称性
DOI：
10.1088/1742-5468/ab11c0
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Vernier E
中科院分区：
文献类型：
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作者：
Vernier E
我们展示了如何Onsager代数，在原来的解决方案中使用的二维伊辛模型，出现作为一个无限维对称的某些自对偶模型，也有一个对称。我们详细描述了最近邻n态时钟链的对称性增强的例子。由于Onsager代数对称性，这些模型的谱具有退化性，对于正整数N，其重数为2 N。我们从量子群代数的非基本表示建立的转移矩阵中明确地构造代数的元素。我们分析了光谱进一步通过使用坐标Bethe anasteries和功能的方法，并表明退化的结果从特殊的精确的n弦解的Bethe方程。我们还发现了一个家庭的交换手征哈密顿，打破简并，并允许铁磁和反铁磁之间的可积插值。
We show how the Onsager algebra, used in the original solution of the two-dimensional Ising model, arises as an infinite-dimensional symmetry of certain self-dual models that also have a symmetry. We describe in detail the example of nearest-neighbour n-state clock chains whose symmetry is enhanced to. As a consequence of the Onsager-algebra symmetry, the spectrum of these models possesses degeneracies with multiplicities 2 N for positive integer N. We construct the elements of the algebra explicitly from transfer matrices built from non-fundamental representations of the quantum-group algebra. We analyse the spectra further by using both the coordinate Bethe ansatz and a functional approach, and show that the degeneracies result from special exact n-string solutions of the Bethe equations. We also find a family of commuting chiral Hamiltonians that break the degeneracies and allow an integrable interpolation between ferro-and antiferromagnets.