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: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:

AcPPBOct 1, 20012 citations

Charge Physics of the Falicov-Kimball Model

P. M. R. Brydon, M. Gulácsi

Bulletin of the American Physical SocietyMar 16, 20060 citations

Falicov-Kimball model and the problem of electronic ferroelectricity

Pavol Farkašovský

The density matrix renormalization group method is used to examine possibilities of electronic ferroelectricity in the spinless Falicov-Kimball model. The model is studied for a wide range of parameters including weak and strong interactions as well as the symmetric and unsymmetric case. In all examined cases the $〈{d}^{+}f〉$ -expectation value vanishes for vanishing hybridization V, indicating that the spinless Falicov-Kimball model does not allow for a ferroelectric ground state with a spontaneous polarization.The density matrix renormalization group method is used to examine possibilities of electronic ferroelectricity in the spinless Falicov-Kimball model. The model is studied for a wide range of parameters including weak and strong interactions as well as the symmetric and unsymmetric case. In all examined cases the $〈{d}^{+}f〉$-expectation value vanishes for vanishing hybridization V, indicating that the spinless Falicov-Kimball model does not allow for a ferroelectric ground state with a spontaneous polarization.

arXiv:cond-mat/0109479Physical review. B, Condensed matterJan 30, 200232 citations

Ground State of the Falicov-Kimball Model

William J. Massano, Jay D. Mancini, Vassilios Fessatidis +1 more

Bulletin of the American Physical SocietyMar 23, 20050 citations

Exact results for the extended Anderson model with Falicov-Kimball interactions

L. G. Sarasúa, M. A. Contínentino

We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension $(d=1).$ Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions $〈{\mathrm{cf}}^{+}〉$ are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension $(d=1).$ Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions $〈{\mathrm{cf}}^{+}〉$ are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.

Physical review. B, Condensed matterJun 20, 200215 citations

〈{d}^{+}f〉

-expectation value vanishes for vanishing hybridization V, indicating that the spinless Falicov-Kimball model does not allow for a ferroelectric ground state with a spontaneous polarization.

We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension

(d=1).

Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions

〈{\mathrm{cf}}^{+}〉

are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.