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Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics

A Monte Carlo study of the spinless Falicov‐Kimball model in the perturbative regime: preliminary results

Jacek Wojtkiewicz, Grzegorz Musiał, L. Dębski

Published Jan 1, 2006• 4 citations
Publisher

Abstract

Abstract Finite‐temperature properties of the Falicov‐Kimball model on the square lattice have been studied in the perturbative regime, i.e. in the case: t = U ≪ 1, where t is the hopping constant and U denotes the Coulomb interaction strength. In our study, we have determined the phase diagram of the model in the second‐order of the perturbation theory, where the antiferromagnetic Ising model in the magnetic field emerges, and partially in the fourth‐order, where it constitutes the Ising model with more complicated frustrated antiferromagnetic interactions. The Monte Carlo method was employed, which proved its accuracy in recent analyses of other spin models, like Ashkin‐Teller model. To determine the type of ordering and phase boundaries, the behavior of Binder cumulants, based on the order parameters under consideration, was analyzed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssc.200562508

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Abstract We show that the histogram method that is widely used in the Monte Carlo simulations for the Ising model, can also be implemented in the simulations carried out for the Falicov–Kimball model. We estimate the systematic errors arising from application of this method and discuss the regimes of model parameters, where these errors are minimal. We apply the histogram method for determining the transition temperature and demonstrate significant advantages over standard simulations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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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)

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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)

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physica status solidi (b)•May 7, 2007•7 citations
Abstract Finite‐temperature properties of the Falicov‐Kimball model on the square lattice have been studied in the perturbative regime, i.e. in the case: t = U ≪ 1, where t is the hopping constant and U denotes the Coulomb interaction strength. In our study, we have determined the phase diagram of the model in the second‐order of the perturbation theory, where the antiferromagnetic Ising model in the magnetic field emerges, and partially in the fourth‐order, where it constitutes the Ising model with more complicated frustrated antiferromagnetic interactions. The Monte Carlo method was employed, which proved its accuracy in recent analyses of other spin models, like Ashkin‐Teller model. To determine the type of ordering and phase boundaries, the behavior of Binder cumulants, based on the order parameters under consideration, was analyzed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Finite-temperature properties of the Falicov-Kimball model on the square lattice have been studied in the perturbative regime, i.e., for t/U⪡1, where t is the hopping constant and U denotes the Coulomb interaction strength. In our study, we have determined the phase diagram of the model in the second-order of the perturbation theory, where the antiferromagnetic Ising model in the magnetic field emerges. In the fourth-order, where our model constitutes the Ising model with more complicated frustrated antiferromagnetic interactions, the sketch of the phase diagram was established. The Monte Carlo method was employed and the behavior of Binder cumulants based on the order parameters was analyzed to determine the type of ordering and phase boundaries in the diagram.
Finite-temperature properties of the Falicov-Kimball model in two approximations were studied in the perturbative regime, i.e. for t/U 1, where t = 1 is the hopping constant and U = 10 denotes the Coulomb interaction strength.In our study, we determined the phase diagram of the model in the second order of the perturbation theory, where it reduces to the antiferromagnetic Ising model in the emergent magnetic field.In the fourth order, where our model constitutes the Ising model with more complicated frustrated antiferromagnetic interactions, the phase diagram was established.The Monte Carlo method was employed to investigate the phase transition lines.The existence of stripe ordering at finite temperatures is proved.
Abstract We show that the histogram method that is widely used in the Monte Carlo simulations for the Ising model, can also be implemented in the simulations carried out for the Falicov–Kimball model. We estimate the systematic errors arising from application of this method and discuss the regimes of model parameters, where these errors are minimal. We apply the histogram method for determining the transition temperature and demonstrate significant advantages over standard simulations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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)
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)