Abstract
We develop exact fermion transformations which can deal with strong local Coulomb repulsions. A new basis is chosen where the effective local repulsion is much smaller, coming from a combination of level separation energies and hybridisation energies. The new representation of fermions with weaker local correlations also has longer range many body effects which can lead to superconducting pairing instabilities of singlet and triplet varieties. The spin half Anderson Lattice is solved approximately near the atomic limit. Magnetism, singlet pairing and triplet pairing all have regimes of relative stability. A canonical single fermion Hamiltonian is introduced for this limit.
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