The Bethe ansatz approach for factorizable centrally extended su(2|2)S-matrices

We consider the Bethe ansatz solution of integrable models interacting through factorized S-matrices based on the central extension of the su(2|2) symmetry. The respective su(2|2)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 su(2|2)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 su(2|2)xsu(2|2)S-matrix. The result for the quantization rule may be of relevance in the study of the energy spectrum of the AdS5xS5 string sigma model in the thermodynamic limit