Algebraic Bethe ansatz for a spin-1/2 quantum linear chain with competing interactions

We propose a generalization of the formula that gives an integrable quantum 1D spin Hamiltonian with nearest-neighbour interactions as a logarithmic d erivative of a vertex model transfer matrix in order to include in this sch eme more realistic integrable models. We compute exactly this generalized f ormula using the R matrix of the XXX model, obtaining the Majumdar-Ghosh Ha miltonian plus a charge-like interaction term. We diagonalize this Hamilton ian using the quantum inverse scattering method and present the Bethe ansat z equations of the model.