ABSTRACT
We present a systematic study of various forms of renormalization that can be applied in the calculation of the self-energy of the Hubbard model within the T-matrix approximation. We compare the exact solutions of the attractive and repulsive Hubbard models, for linear chains of lengths up to eight sites, with all possible taxonomies of the T-matrix approximation. For the attractive Hubbard model, the success of a minimally self-consistent theory found earlier in the atomic limit (Verga et al 2005 Phys. Rev. B 71 155111) is not maintained for finite clusters unless one is in the very strong correlation limit. For the repulsive model, in the weak correlation limit at low electronic densities-that is, where one would expect a self-consistent T-matrix theory to be adequate-we find the fully renormalized theory to be most successful. In our studies we employ a modified Hubbard interaction that eliminates all Hartree diagrams, an idea which was proposed earlier (Zlatic et al 2000 Phys. Rev. B 63 035104).
ABSTRACT
The compound LiAlyTi2-yO4 undergoes a metal-to-insulator transition for yc approximately 0.33. It is known that disorder alone is insufficient to explain this transition; e.g., a quantum site percolation model predicts yc approximately 0.8. We have included (Hubbard) electronic interactions into a model of this compound, using a real-space Hartree-Fock approach that achieves self-consistency at every site, and have found that for a Hubbard energy equal to 1.5 times the non-interacting bandwidth one obtains yc approximately 0.3. Further, with increasing Hubbard energy we find an Altshuler-Aronov suppression of the density of states, deltaN(epsilon) approximately square root /epsilon-epsilonF/, that reduces the density of states at the Fermi energy to zero at the critical Hubbard interaction. Using this ratio of correlation to hopping energy one is led to a prediction of the near-neighbor superexchange (J/t approximately 1/3) which is similar to that for the cuprate superconductors.