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Modern Physics Letters B

THE SPINLESS FALICOV–KIMBALL MODEL AWAY FROM HALF-FILLING

Štefan Gál

Published Jun 30, 1999• 4 citations
Publisher

Abstract

The one-dimensional spinless Falicov–Kimball (FKM) model is studied in the strong coupling limit away from half-filling. The small-cluster exact-diagonalization calculations are employed to obtain valence transitions in the ground state and for finite temperatures. It is found that in the ground state, the model describes continuous valence transitions for small band-fillings and both continuous and discontinuous transitions near half-filling. At finite temperatures, only continuous valence transitions are obtained. The valence is integer at low temperatures for small band-fillings and in other cases, it takes only intermediate values.

DOI
10.1142/s0217984999000658

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The one-dimensional spinless Falicov–Kimball (FKM) model is studied in the strong coupling limit away from half-filling. The small-cluster exact-diagonalization calculations are employed to obtain valence transitions in the ground state and for finite temperatures. It is found that in the ground state, the model describes continuous valence transitions for small band-fillings and both continuous and discontinuous transitions near half-filling. At finite temperatures, only continuous valence transitions are obtained. The valence is integer at low temperatures for small band-fillings and in other cases, it takes only intermediate values.
We use strong-coupling perturbation theory and the extrapolation of small-cluster exact-diagonalization calculations to describe the ground-state properties and possible intermediate-valence transitions of the spinless Falicov-Kimball model with a generalized type of hopping. It is shown that, even for relatively small values of the interaction strength, the Falicov-Kimball model undergoes only a few (discrete) intermediate-valence transitions, and this result is demonstrated to be independent of finite-size effects.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. It is shown that in the half-filled band case the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional Falicov-Kimball model (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition. Outside half-filling correlated hopping stabilizes the segregated phase in the ground-state, however, the nature of the ground-state remains qualitatively unchanged.
The thermodynamic properties of the extended Falicov-Kimball model (FKM) for spinless fermions are studied as a function of temperature, doping, and interlevel spacing on the two-dimensional lattice. Thermodynamic quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of $4\ifmmode\times\else\texttimes\fi{}4$ sites. Changes of the thermodynamic properties are studied as the system evolves from its symmetric limit represented by the original Hubbard model to the other limiting case, which corresponds to the original FKM for spinless fermions. Our results indicate that valence transition exists in the extended Falicov-Kimball model.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. 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 (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition, even in the half-filled band case.
We examine the spinless one-dimensional Falicov-Kimball model (FKM) below half filling, addressing both the binary alloy and valence transition interpretations of the model. Using a nonperturbative technique, we derive an effective Hamiltonian for the occupation of the localized orbitals, providing a comprehensive description of charge order in the FKM. In particular, we uncover the contradictory ordering roles of the forwardscattering and backscattering itinerant electrons: the latter are responsible for the crystalline phases, while the former produces the phase separation. We find an Ising model describes the transition between the phase separated state and the crystalline phases; for weak coupling we present the critical line equation, finding excellent agreement with numerical results. We consider several extensions of the FKM that preserve the classical nature of the localized states. We also investigate a parallel between the FKM and the Kondo lattice model, suggesting a close relationship based upon the similar orthogonality catastrophe physics of the associated single-impurity models.