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physica status solidi (b)

Phase transitions in the two‐dimensional Falicov–Kimball model on the triangular lattice

Hana Čenčariková, Pavol Farkašovský

Published Feb 14, 2007• 6 citations
Publisher

Abstract

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)

DOI
10.1002/pssb.200642496

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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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Abstract We present a systematic investigation of the stability of the phase diagram of the spinless Falicov–Kimball model on two-dimensional non-bipartite lattices, the triangular and kagome lattices, using Markov-chain Monte Carlo simulations. Three filling or chemical potential conditions are examined: fixed chemical potentials ( $$\mu _f = \mu _c = U/2$$ μ f = μ c = U / 2 ), “generalized” half-filling ( $$\bar{n}_f = 1/3$$ n ¯ f = 1 / 3 , $$\bar{n}_c = 2/3$$ n ¯ c = 2 / 3 ), and conventional half-filling ( $$\bar{n}_f = \bar{n}_c = 1/2$$ n ¯ f = n ¯ c = 1 / 2 ). For each condition, the effects of a perturbatively small next-nearest-neighbor hopping are studied. On the triangular lattice, Anderson insulator, Mott insulator, and charge-density wave (CDW) phases are found in all cases, with the CDW driven by Coulomb interaction-mediated nesting. Evidence for a charge-liquid regime is found in the region between the weakly correlated regime and the CDW, characterized by competing charge-ordering wavevectors and the absence of universal scaling behavior, whose extent shrinks progressively from the grand-canonical to the conventional half-filling condition. On the kagome lattice, the CDW phase is completely absent; instead, an insulating ground state, plausibly of the Mott type, is found, with signatures of a possible quantum phase transition at zero temperature. Our results establish the crucial role of lattice geometry and particle-hole symmetry breaking in shaping the phase diagram of correlated electron systems. Graphical abstract The 2d triangular lattice (left) and the 2d kagome lattice (right) with their unit cells highlighted. Bottom: The corresponding phase diagram of the Falicov-Kimball model (FKM) on each lattice, illustrating the non-Fermi liquid (nFL), charge-density wave (CDW), Anderson insulator (AI) and Mott insulator (MI) regimes.

arXiv:2608.28898•The European Physical Journal B•Sep 1, 2026•0 citations
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)
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)
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)
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.
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.
Abstract We present a systematic investigation of the stability of the phase diagram of the spinless Falicov–Kimball model on two-dimensional non-bipartite lattices, the triangular and kagome lattices, using Markov-chain Monte Carlo simulations. Three filling or chemical potential conditions are examined: fixed chemical potentials ( μf=μc=U/2\mu _f = \mu _c = U/2μf​=μc​=U/2 μ f = μ c = U / 2 ), “generalized” half-filling ( nˉf=1/3\bar{n}_f = 1/3nˉf​=1/3 n ¯ f = 1 / 3 , nˉc=2/3\bar{n}_c = 2/3nˉc​=2/3 n ¯ c = 2 / 3 ), and conventional half-filling ( nˉf=nˉc=1/2\bar{n}_f = \bar{n}_c = 1/2nˉf​=nˉc​=1/2 n ¯ f = n ¯ c = 1 / 2 ). For each condition, the effects of a perturbatively small next-nearest-neighbor hopping are studied. On the triangular lattice, Anderson insulator, Mott insulator, and charge-density wave (CDW) phases are found in all cases, with the CDW driven by Coulomb interaction-mediated nesting. Evidence for a charge-liquid regime is found in the region between the weakly correlated regime and the CDW, characterized by competing charge-ordering wavevectors and the absence of universal scaling behavior, whose extent shrinks progressively from the grand-canonical to the conventional half-filling condition. On the kagome lattice, the CDW phase is completely absent; instead, an insulating ground state, plausibly of the Mott type, is found, with signatures of a possible quantum phase transition at zero temperature. Our results establish the crucial role of lattice geometry and particle-hole symmetry breaking in shaping the phase diagram of correlated electron systems. Graphical abstract The 2d triangular lattice (left) and the 2d kagome lattice (right) with their unit cells highlighted. Bottom: The corresponding phase diagram of the Falicov-Kimball model (FKM) on each lattice, illustrating the non-Fermi liquid (nFL), charge-density wave (CDW), Anderson insulator (AI) and Mott insulator (MI) regimes.