Abstract
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. Assuming that the monodromy matrix of the model can be expanded into series with respect to the inverse spectral parameter, we define zero modes of the monodromy matrix entries as the first nontrivial coefficients of this series. Using these zero modes we establish new relations between form factors of the elements of the monodromy matrix. We prove that all of them can be obtained from the form factor of a diagonal matrix element in special limits of Bethe parameters. As a result we obtain determinant representations for form factors of all the entries of the monodromy matrix.
Highlights
The algebraic Bethe ansatz is a powerful method of studying quantum integrable models [1,2,3,4]
One more relationship between different form factors appears due to the isomorphism (2.5), that implies the following transform of Bethe vectors: φ Ba,b(u; v) = Bb,a(−v; −u), φ Ca,b(u; v) = Cb,a(−v; −u)
In this paper we have developed a new method of calculation of form factors of the monodromy matrix entries in GL(3)-invariant integrable models
Summary
The algebraic Bethe ansatz is a powerful method of studying quantum integrable models [1,2,3,4]. If one of these vectors is an eigenvector of the quantum Hamiltonian, for the models possessing GL(2) symmetry or its q-deformation the corresponding scalar products were calculated in [20] In this way one can obtain determinant representations for form factors [9, 10, 21]. It is applicable to quantum integrable models whose monodromy matrix T (z) can be expanded into a series in the inverse spectral parameter z−1 [24, 25] We call this approach the zero modes method. In appendix B we check relations between different form factors via explicit determinant formulas
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