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Acta Physica Polonica A

One-Dimensional Falicov-Kimball Model in the Strong Coupling Limit

Pavol Farkašovský, Ivan Batko

Published Feb 1, 1994• 0 citations
Publisher

Abstract

We studied the ground state properties of the one-dimensional Falicov-Kimball model in the strong coupling limit for special periodic and aperiodic configurations of ions.The ground state phase diagrams of the model for nearest neighbor and next nearest neighbor hopping are discussed.
DOI
10.12693/aphyspola.85.307

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The authors have studied energetic and structural ground-state properties of the one-dimensional Falicov-Kimball model in the strong-coupling limit. Using standard perturbation theory they recover some results already obtained (the phase segregation at large interactions) and present some new results concerning the ground state, e.,g., the analytic expression for the boundary, below which the segregated configuration cannot be the ground state, and the phase diagram of the model calculated for special periodic (aperiodic) configurations of ions and for the case when the ion concentration goes to zero.
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We have studied the ground state properties of the Falicov-Kimball model with unconstrained hopping. It is shown that the model still behaves non-trivially, although it no longer depends on the actual lattice structure and dimensionality of the system. For arbitrary ion configurations with total number of ions Ni, we have been able to determine domains in the plane of the chemical potentials of electrons and ions where these ion configurations are ground states. The phase diagram of the model is discussed.
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:
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