Spinless Falicov-Kimball Model Research Articles

Ground state properties of the spinless Falicov-Kimball model: Crystallization and metal-insulator transitions off the hole-particle symmetry point

Properties of grounds states of an itinerant electron model (which can be regarded as the one-band, spinless Falicov-Kimball model) beyond the hole-particle symmetry point are studied. The underlying lattice is chosen to be a square lattice. Using exact and numerical arguments it is shown that when the density of band electrons is varied different sorts of periodic configurations of localized particles (f-electrons) minimize the energy. The one- particle densities of states of the band electrons corresponding to these configurations are presented. The system can be a metal or an insulator accordingly. Moreover, for some densities of band electrons a metal-insulator transition, driven by the unique parameter of the system, takes place. The importance of many-body effects is revealed.

Ground state properties of a spinless Falicov-Kimball model; additional features

We have studied some energetic and structural ground state properties of a spinless Falicov-Kimball model. Using a method based on “Tchebycheff-Markoff inequalities”, we have calculated sharp upper and lower bounds for the ground state energy. These calculations lead to rigorous results for a special range of parameters, where we are able to give the exactf-level occupation pattern for a square lattice. The results for the “symmetric” case, where a superstructure occurs leading to a metal-insulator transition, have already been published. In this paper we present some additional results also for the “unsymmetric case” and study valence-transitions for fixed particle-number.

Exact results for the distribution of thef-level ground state occupation in the spinless Falicov-Kimball model

We present sharp upper and lower bounds for the ground state energy of the spinless Falicov-Kimball model, leading to rigorous results for a special choice of parameters. In this ‘symmetric’ case we are able to give the exactf-level occupation pattern for a square lattice. A superstructure occurs, leading to a metal-insulator transition.

Alloy analog approximation for the spinless Falicov-Kimball model with hybridization

We study the Falicov-Kimball model with a hybridization between localized and band electron states in the alloy analog approximation. Within this treatment an effective randomness has to be taken into account for the conduction electrons, for the localized electrons, and for the hybridization. This “disordered system” is treated within the coherent potential approximation. Only a continuous dependence of the localized level occupation number n ff on the level position E o is obtained. Comparing our results with the results of different Hartree-Fock approximations we show that in general the Hartree-Fock solution yields an unrealistically steep n ff (E o) dependence. Furthermore it is shown that the discontinuous valence transitions reported frequently in the literature on that model are clearly an artifact of the underlying mean-field like decoupling.