The extrapolation of finite-cluster calculations is used to examine ground-state properties of the one-dimensional Falicov–Kimball model with correlated hopping. It is shown that the correlated hopping strongly influences both the valence transitions and the conducting properties of the model and so it should not be neglected in the correct description of materials with correlated electrons. This is illustrated for two selected values of the Coulomb interaction that represent typical behavior of the model for small and intermediate (strong) interactions. In both cases the insulator–metal transitions (accompanied by continuous or discontinuous valence transitions) induced by correlated hopping are observed.
The interaction between the bosonic excitations as well as between the fermionic ones in the RVB systems with the (extended) Hubbard Hamiltonian were studied by means of the slave boson technique and the perturbation theory. The corresponding effective Hamiltonians have been found. It was shown, in particular, that in the RVB system with two interpenetrating sublattices there exists the effective attraction between two holons of different kinds as well as between two spinions of different kinds in the singlet state.