Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
In the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric gl(2)⊗gl(2)-valued Cartan-non-invariant classical r-matrices with spectral parameters. We consider the two families of these r-matrices, namely, the two non-standard rational r-matrices twisted with...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-06-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321321001218 |
| Summary: | In the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric gl(2)⊗gl(2)-valued Cartan-non-invariant classical r-matrices with spectral parameters. We consider the two families of these r-matrices, namely, the two non-standard rational r-matrices twisted with the help of second order automorphisms and realize the algebraic Bethe ansatz method for them. We study physically important examples of the Gaudin-type and BCS-type systems associated with these r-matrices and obtain explicitly the Bethe vectors and the spectrum for the corresponding quantum hamiltonians in terms of solutions of Bethe equations. |
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| ISSN: | 0550-3213 |