“Generalized” algebraic Bethe ansatz, Gaudin-type models and Z_p-graded classical r-matrices

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• 作者：T. Skrypnyk^a ; ^b ; ^{taras.skrypnyk@unimib.it} ; ^{tskrypnyk@imath.kiev.ua}
• 刊名：Nuclear Physics B
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：913
• 期：Complete
• 页码：327-356
• 全文大小：425 K
• 卷排序：913

文摘

We consider quantum integrable systems associated with reductive Lie algebra gl(n)gl(n) and Cartan-invariant non-skew-symmetric classical r-matrices. We show that under certain restrictions on the form of classical r  -matrices “nested” or “hierarchical” Bethe ansatz usually based on a chain of subalgebras gl(n)⊃gl(n−1)⊃...⊃gl(1)gl(n)⊃gl(n−1)⊃...⊃gl(1) is generalized onto the other chains or “hierarchies” of subalgebras. We show that among the r  -matrices satisfying such the restrictions there are “twisted” or ZpZp-graded non-skew-symmetric classical r  -matrices. We consider in detail example of the generalized Gaudin models with and without external magnetic field associated with ZpZp-graded non-skew-symmetric classical r  -matrices and find the spectrum of the corresponding Gaudin-type hamiltonians using nested Bethe ansatz scheme and a chain of subalgebras gl(n)⊃gl(n−n1)⊃gl(n−n1−n2)⊃gl(n−(n1+...+np−1))gl(n)⊃gl(n−n1)⊃gl(n−n1−n2)⊃gl(n−(n1+...+np−1)), where n1+n2+...+np=nn1+n2+...+np=n.