Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models

Skrypnyk, T.; Manojlović, Nenad

http://hdl.handle.net/10400.1/16335

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Authors

Skrypnyk, T.

Manojlović, Nenad

Abstract(s)

In the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric gl(2) circle times 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. (C) 2021 The Author(s). Published by Elsevier B.V.