Physics – Mathematical Physics
Scientific paper
2012-04-10
Physics
Mathematical Physics
19 pages, 7 figures
Scientific paper
We consider a generalized model with SU(3)-invariant R-matrix, and review the nested Bethe Ansatz for constructing eigenvectors of the transfer matrix. A sum formula for the scalar product between generic Bethe vectors, originally obtained by Reshetikhin [1], is discussed. This formula depends on a certain partition function Z(\{\lambda\},\{\mu\}|\{w\},\{v\}), which we evaluate explicitly. In the limit when the variables \{\mu\} or \{v\} approach infinity, this object reduces to the domain wall partition function of the six-vertex model Z(\{\lambda\}|\{w\}). Using this fact, we obtain a new expression for the off-shell scalar product (between a generic Bethe vector and a Bethe eigenvector), in the case when one set of Bethe variables tends to infinity. The expression obtained is a product of determinants, one of which is the Slavnov determinant from SU(2) theory. It extends a result of Caetano and Vieira [2].
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