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arXiv:cond-mat/0107105 · Journal of Physics Condensed Matter

Ground-state properties of the Falicov-Kimball model with correlated hopping in two dimensions

Pavol Farkašovský, Natália Tomašovičová

Published Dec 24, 2001• 16 citations
arXivHTMLPDF

Abstract

A new numerical method, recently developed to study ground states of the Falicov-Kimball model (FKM), is used to examine the effects of correlated hopping on the ground-state properties of this model in two dimensions. It is shown that the ground-state phase diagram as well as the picture of metal-insulator transitions found for the conventional FKM (without correlated hopping) are substantially 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 strong-coupling limit, where the ground states of the conventional FKM are insulating for all f-electron densities.

DOI
10.1088/0953-8984/14/3/318

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A new numerical method, recently developed to study ground states of the Falicov-Kimball model (FKM), is used to examine the effects of correlated hopping on the ground-state properties of this model in two dimensions. It is shown that the ground-state phase diagram as well as the picture of metal-insulator transitions found for the conventional FKM (without correlated hopping) are substantially 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 strong-coupling limit, where the ground states of the conventional FKM are insulating for all f-electron densities.
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.
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.
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.
Abstract The extrapolation of finite cluster calculations is used to study effects of correlated hopping on the ground‐state properties of the two‐dimensional Falicov–Kimball model (FKM). It is shown that the ground‐state phase diagram as well as the picture of valence transitions found for the conventional FKM (without correlated hopping) are strongly changed when the correlated hopping term is added. In particular, it is found that non‐zero values of correlated hopping stabilize a new type of spatial charge ordering, the axial stripes, for a wide range of model parameters. This result indicates that the competition between the kinetic energy, the on‐site Coulomb energy and the correlated hopping term can be an alternative mechanism leading to stripe formation in the strongly correlated electron systems. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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:
Combined effects of correlated electron hopping, electron correlations and orbital magnetic field are studied on ground state properties of spinless Falicov-Kimball model (FKM). Results are obtained for finite size triangular lattice with periodic boundary conditions using numerical diagonalization and Monte-Carlo simulation techniques. It is found that the ground state configurations of electrons strongly depend on correlated electron hopping, onsite Coulomb interaction and orbital magnetic field. Several interesting configurations e.g. regular, segregated, axial and diagonal striped and hexagonal phases are found with change in correlated hopping and magnetic field. Study of density of states reveals that magnetic field induces a metal to insulator transition accompanied by segregated phase to an ordered phase. These results are applicable to the systems of recent interest like GdI2, NaTiO2 and MgV2O4 and can also be seen experimentally in cold atomic set up.