Correlation effects in high-Tc superconductors and heavy fermion compounds

This paper describes certain aspects of Highly Correlated Systems (HCS) such as high Tc superconductors (HTSC) and some new class of Heavy Fermion (HF) systems which have been studied recently. The problem is discussed on how the charge and spin degrees of freedom participate in the specific character of superconductivity in the copper oxides and competition of the magnetism and Kondo screening in heavy fermions. The electronic structure and possible superconducting mechanisms of HTSC compounds are discussed. The similarity and dissimilarity with HF compounds is pointed out. It is shown that the spins and carriers in the copper oxides are coupled in a very nontrivial way in order to introduce the discussion and the comparison of the Emery model, the t - J-model and the Kondo-Heisenberg model. It concerns attempts to derive from fundamental multi-band Hamiltonian the reduced effective Hamiltonians to extract and separate the relevant low-energy physics. A short review of the arguments which seem to support the spin-polaron pairing mechanism in HTSC are presented. Many other topics like the idea of mixed valence states in oxides, the role of charge transfer (CT) excitations, phase separation, self-consistent nonperturbative technique, etc. are also discussed. (author). 161 refs