Strongly Correlated Systems

Abstract

Electron–electron interactions were mostly treated at the mean-field level in the previous chapters. Restricting ourselves to the Hartree–Fock approach or the RPA seems to be justified if the interaction term is small compared to the kinetic energy or, more precisely, when the Coulomb repulsion U resulting from the intra-atomic interaction is small compared to the bandwidth W. The band structure and the spectrum of single-particle states can then be determined using a one-particle potential which includes exchange. As we have seen in Chapter 28, there are no correlations between electrons of opposite spin in the Hartree–Fock approximation. The Fermi hole (exchange hole), the dip in the pair distribution function of parallel-spin electrons, is due to the Pauli principle. The corrections beyond the Hartree–Fock approximation are known as the correlation contributions. They can be treated as weak perturbations when U ≪W. This is not always the case in physically realistic systems. Often the two energy scales set by the bandwidth and the Coulomb repulsion are quite comparable or the relation is even inverted. Such systems are known as strongly correlated systems. This is the case in particular in compounds containing lanthanoid (rare-earth) ions1 with localized 4f electrons or actinoids with incomplete 5f shells.2