Self-interaction-corrected density-functional formalism. I. Ground-state properties of the Hubbard-Peierls model

We present detailed studies of the self-interaction-corrected local-spin-density method. As an application, we consider ground-state properties of a highly correlated many-electron system interacting with phonons, namely, the one- and two-dimensional Hubbard-Peierls model. An efficient minimization method is presented which allows one to find fully self-consistent solutions to the self-interaction-corrected local-spin-density total-energy functional without assuming any symmetry of the one-electron states. Charge- and spin-correlation functions, the energy gap, and phonon-induced electronic energy gains for the two-dimensional Hubbard-Peierls model are in significantly better agreement with numerically exact results than the standard local-density method. Noticeably, we find that phonons tend to de- stabilize the antiferromagnetic ground state in two dimensions and show a negative-U behavior in the energy gap, in contrast to the situation in one dimension. This is relevant for the theory of high-temperature superconductivity.