On the symmetries of the Hubbard model: application to finite-size clusters

We evaluate the density of states of the Hubbard model at half filling on a four-site cluster with periodic boundary conditions. The results are obtained from an exact diagonalization study of the model, where theSU(2) symmetry, the Yang\(\widetilde{SU}(2)\) pseudospin symmetry and the translational invariance of the Hamiltonian are explicitly taken into account.