The Bethe ansatz approach for factorizable centrally extended image S-matrices Original Research Article

We consider the Bethe ansatz solution of integrable models interacting through factorized S-matrices based on the central extension of the image symmetry. The respective image R-matrix is explicitly related to that of the covering Hubbard model through a spectral parameter dependent transformation. This mapping allows us to diagonalize inhomogeneous transfer matrices whose statistical weights are given in terms of image S-matrices by the algebraic Bethe ansatz. As a consequence of that we derive the quantization condition on the circle for the asymptotic momenta of particles scattering by the image S-matrix. The result for the quantization rule may be of relevance in the study of the energy spectrum of the image string sigma model in the thermodynamic limit.