Narrow Results

The f and d electron density of states of the one-dimensional Falicov–Kimball model are studied in the weak-coupling limit by exact diagonalization calculations. The resultant behaviors are used to examine the d electron gap (Δ_d), the f electron gap (Δ_f), and the fd electron gap (Δ_fd) as functions of the f level energy E_f and hybridization V. It is shown that the spinless Falicov–Kimball model behaves fully differently for zero and finite hybridization between f and d states. At zero hybridization the energy gaps do not coincide (Δ_d ≠ Δ_f ≠ Δ_fd), and the activation gap Δ_fd vanishes discontinuously at some critical value of the f level energy E_fc. On the other hand, at finite hybridization all energy gaps coincide and vanish continuously at the insulator-metal transition point E_f = E_fc. The importance of these results for a description of real materials is discussed.

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 influence of doping on valence and metal-insulator transitions in the spinless Falicov–Kimball model is studied by the well-controlled numerical method. Two types of doping are examined, and namely, the substitution of rare-earth ions by non-magnetic ions that introduce (i) one or (ii) no additional electron (per non-magnetic ion) into the conduction band. It is found that the first type of substitution increases the average f-state occupancy of rare-earth ions, whereas the second type of substitution has the opposite effect. In both cases valence changes are accompanied by a doping induced insulator-metal transition. The results obtained are used to describe valence and metal-insulator transitions in the samarium hexaboride solid solutions.

A combination of small-cluster exact diagonalizations and a well-controlled approximative method is used to study the ground states of the Falicov–Kimball model extended by nonlocal Coulomb interaction (U_non). It is shown that the ground-state phase diagram as well as the picture of valence and metal–insulator transitions found for the conventional Falicov–Kimball model are strongly changed when the nonlocal Coulomb interaction is added. This is illustrated for three selected values of the on-site Coulomb interaction (U) that represent typical behaviors of the model for small, intermediate and strong interactions. A number of remarkable results are found: (i) the phase separation takes place for a wide range of U_non in all three interaction limits; (ii) in the weak and intermediate coupling limit, the model exhibits the nonlocal Coulomb interaction–induced insulator–metal transition; (iii) depending on the value of U_non, the model is able to describe both the continuous and the discontinuous changes of the f-electron occupation number; (iv) new types of inhomogeneous charge ordering (including various types of axial and diagonal stripes) are observed for nonzero U_non.