This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of the classical "covering" Hubbard model within the algebraic Bethe Ansatz framework. The fundamental commutation rules exhibit a hidden 6-vertex symmetry which plays a crucial role in the whole algebraic construction. Next we apply this formalism to study the SU (2) highest weights properties of the eigenvectors and the solution of a related coupled spin model with twisted boundary conditions. The machinery developed in this paper is applicable to many other models, and as an example we present the algebraic solution of the Bariev XY coupled model.

In this paper we study isotropic integrable systems based on the braid-monoid algebra.These systems constitute a large family of rational multistate vertex models and are realized in terms of the B n , C n and D n Lie algebra and by the superalgebra Osp(n|2m).We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvalues of the transfer matrix associated to the B n , C n , D n , Osp(2n − 1|2), Osp(2|2n − 2), Osp(2n − 2|2) and Osp(1|2n) models. The corresponding Bethe Ansatz equations can be formulated in terms of the root structure of the underlying algebra.

We formulate in terms of the quantum inverse scattering method the algebraic Bethe ansatz solution of the one-dimensional Hubbard model. The method developed is based on a new set of commutation relations which encodes a hidden symmetry of 6-vertex type.

We formulate in terms of the quantum inverse scattering method the exact solution of a spl(2|1) invariant vertex model recently introduced in the literature. The corresponding transfer matrix is diagonalized by using the algebraic (nested) Bethe ansatz approach.The ground state structure is investigated and we argue that a Pokrovsky-Talapov transition is favored for certain value of the 4-dimensional spl(2|1) parameter.

We consider the exact solution of a model of correlated electrons based on the superalgebra Osp(2|2). The corresponding Bethe ansatz equations have an interesting form.We derive an expression for the ground state energy at half filling. We also present the eigenvalue of the transfer matrix commuting with the Hamiltonian.