Many unconventional pairing mechanisms of electronic origin have been proposed for superconductivity in heavy fermion compounds and high Tc superconductors. While the measured Fermi surfaces of UPt3 and YBa2Cu3O7 seem to agree with the predictions of band theory and experiment which indicate the limitation of the local density approximation and the important role of quantum charge or spin fluctuations. Here, they discuss the origins of these discrepancies based on their understanding of the Hubbard/Anderson model Hamiltonian. Both band structure calculations and model simulations are essential to understand the computer programs for finite temperature Monte-Carlo simulations, as well as a new efficient algorithm for zero- temperature variational Monte-Carlo simulations in which a Gutzwiller projection operator is used to restrict charge fluctuations in noninteracting wave functions. They will continue along these lines to (1) study the novel properties in systems of almost-localized Fermi liquids, and (2) develop techniques for first principle variational quantum Monte-Carlo simulations. In particular, they will investigate the ground state properties of Fe, where the magnetic energy was underestimated by the local-density approximation, and therefore a wrong ground state crystal structure was predicted.
