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Physical review. B, Condensed matter

Finite-temperature properties of the generalized Falicov-Kimball model

Samir El Shawish, J. Bonča, Cristian D. Batista

Published Nov 18, 2003• 6 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.68.195112

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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×\else\texttimes\fi44\ifmmode\times\else\texttimes\fi{}44\ifmmode×\else\texttimes\fi4 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.
Thermodynamic properties of the spin-dependent Falicov-Kimball model are studied on a triangular lattice for one-fourth filled case. Numerical diagonalization and Monte-Carlo simulation are used to study the thermodynamic properties. Continuous phase transitions are observed at finite temperature. We have observed that critical temperature (Tc) increases with the increase in on-site Coulomb correlation IJ. The second order nature of die transition is also revealed from the temperature dependence of specific heat.
Two-dimensional spinless Falicov-Kimball model (FKM) with correlated hopping is studied perturbatively in the limit of large on-site Coulomb interaction U. In the half filled case (i.e., ${\ensuremath{\rho}}_{i}+{\ensuremath{\rho}}_{e}=1,$ where ${\ensuremath{\rho}}_{i},{\ensuremath{\rho}}_{e}$ are densities of ions and electrons, respectively) the effective Hamiltonian in spin variables is derived up to terms proportional to ${U}^{\ensuremath{-}3}.$ Unlike the simplest FKM case, it contains odd parity terms (resulting from the correlated hopping) in addition to even parity ones. The ground-state phase diagram of the effective Hamiltonian is examined in the (a/t,h)(a/t,h)(a/t,h) plane, where a/ta/ta/t is a parameter characterizing strength of the correlated hopping and h is a difference of chemical potentials of two sorts of particles present in the system. It appears to be asymmetric with respect to the change $\stackrel{\ensuremath{\rightarrow}}{h}\ensuremath{-}h$ and an additional ordered phase is found for a certain interval of a/t.a/t.a/t.
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.
The finite-temperature properties of the three-dimensional Falicov-Kimball model are studied in the symmetric case using the classical Monte-Carlo method. Analysing the temperature dependence of the specific heat C V,N we have found that the system exhibits the phase transition from the low-temperature ordered phase to the high-temperature disordered phase. The critical temperature of the phase transition is calculated numerically from the position of the maximum of C V,N and it is shown that its value in the three-dimensional case is considerably enhanced in comparison to the two-dimensional case. In addition, the temperature dependence of the itinerant electron density of states (DOS) is analysed. For very low-temperatures we have observed a formation of fine structure inside the principal gap that transforms to a pseudo-gap at higher temperatures and becomes temperature independent for sufficiently large temperatures. In this temperature region we have calculated DOS for different Coulomb interactions and found the Mott-Hubbard metal-insulator transition.
Both canonical and grand canonical phase diagrams of the one dimensional Falicov-Kimball model (FKM) with correlated hopping are presented for several values of the model parameters. Using the method of restricted phase diagrams the system has been studied in the thermodynamic limit. As compare to the conventional FKM, the diagrams exhibit a loss of the particle-hole symmetry. PACS D5.30.Fk, 71.30+h As the simplest, still non-trivial model of highly correlated electron systems, the Falicov-Kimball model (FKM) attracts growing attention among solid state physicists. It can describe variety of the most intriguing cooperative phenomena, as metal-insulator transition, mixed-valence phenomenon etc. (see e.g. the review [1]). The model deals with itinerant particles (electrons) that can hope between nearest-neighbor sites. Some of lattice sites are occupied by non-movable particles, playing a role of ions or localized electrons; we call them ”ions”. The only interaction in the system is the on-site, Coulomb-type interaction between the electrons and the ions. The interaction generates long-range correlations between the ions. The model has been investigated thoroughly in nineties. Numerous approximate results supplemented with some exact and rigorous statements reported up to now provide a good basis for further extensions of the model towards more realistic physical situations. These include the discussed here model with correlated hopping, according to which the electron hopping rate depends on occupations of relevant sites. The Hamiltonian of the FKM with correlated hopping reads: