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physica status solidi (b)

The influence of correlated hopping on the ground‐state properties of the two‐dimensional Falicov–Kimball model

Hana Čenčariková, Pavol Farkašovský

Published Jul 12, 2005• 6 citations
Publisher

Abstract

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)

DOI
10.1002/pssb.200540075

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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)
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.
Abstract A recently developed numerical method, based on the modification of exact diagonalization calculations, is used to study the ground‐state properties of the spinless Falicov–Kimball model on the triangular lattice. The phase diagram as well as the valence and metal–insulator transitions are analysed and compared with results of the conventional Falicov–Kimball model on the square lattice. It is shown that the different cluster geometry leads to various changes in basic characteristics of the model. In particular, the triangular lattice destroys the symmetry of the phase diagram as well as the valence transitions, and stabilizes the new types of spatial charge ordering – the axial stripes and the phase separated distributions of localized f ‐electrons. Studying the conducting properties of the Falicov–Kimball model on the triangular lattice, the Mott‐Hubbard transition has been observed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
The extrapolation of finite-cluster calculations is used to examine ground-state properties of the one-dimensional Falicov–Kimball model with correlated hopping. It is shown that the correlated hopping strongly influences both the valence transitions and the conducting properties of the model and so it should not be neglected in the correct description of materials with correlated electrons. This is illustrated for two selected values of the Coulomb interaction that represent typical behavior of the model for small and intermediate (strong) interactions. In both cases the insulator–metal transitions (accompanied by continuous or discontinuous valence transitions) induced by correlated hopping are observed.
Abstract The ground‐state properties of the three‐dimensional spinless Falicov‐Kimball model are studied by a wellcontrolled numerical method. The results obtained are used to categorize the ground‐state configurations according to common features for weak, intermediate and strong interactions. It is shown that only a few configuration types form the basic structure of the phase diagram. In particular, the largest regions of stability correspond to phase segregated configurations, striped configurations and configurations in which electrons are distributed in diagonal planes with incomplete chessboard structure. Near half‐filling, mixtures of two phases with complete and incomplete chessboard structure are determined. In addition, the picture of metal‐insulator transitions is presented. The relevance of these results for a description of real material is discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)