Several researchers, including myself, discovered that in the high dimensional limit, the solution of these lattice models may be mapped onto a self consistently embedded impurity problem. I developed a numerical solution to this formalism, and together with collaborators, I used this method to provide the first numerically exact solutions of the Hubbard, periodic, Anderson, two-channel Kondo, and Holstein lattice models in the thermodynamic limit for dimensionality greater than one.
For the Hubbard model, we found that the high-temperature NMR, resistivity, optical conductivity and Hall coefficient display anomalies similar to those found in the cuprate superconductors, confirming the assertion by Zhang, Rice and Anderson that the Hubbard Model is appropriate to describe the normal state of the cuprates.
We have shown that the asymmetric Periodic Anderson model's screening is protracted when compared to the impurity model with the same parameters. In many ways, the protracted behavior found in the PAM is related to the ideas of exhaustion put forth by Nozieres. However, there are important quantitative differences between the predictions of Nozieres and our calculations. We later confirmed these results using zero temperature NRG calculations, and made predictions for the optical conductivity. Some recent photoemission, optical conductivity, and susceptibility experiments are consistent with these results. However, the experimental controversy remains.
For the two-channel Kondo lattice, we find no tendency towards electronic coherence; rather, when there is no phase transition, its low-temperature state appears to be a non-Fermi liquid with a large negative magnetoresistance. The phase diagram also contains antiferromagnetic and a new novel odd-frequency superconducting ground state. I believe that this is the first such observation of odd-frequency superconductivity in a nontrivial physical model.