Application of the global SO(4) symmetry in the diagonalization of translationally invariant correlated electron models

We present a method for the simultaneous implementation of the spin symmetry, the pseudospin symmetry and the translational invariance in models for correlated electron systems on finite-size clusters. The application of this method leads to a significative reduction of the size of the Hamiltonian matrix blocks, thus considerably simplifying the diagonalization procedure. We illustrate the method solving exactly the Hubbard model on a 8-site chain in the Hilbert subspaces labelled by the eigenvalues of the spin, the pseudospin and the momentum operators. Some relevant thermodynamical quantities, such as the specific heat and the static magnetic susceptibility, are then evaluated and a brief discussion on the tendency of the model to exhibit ferromagnetism is also presented.