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Physical review. B, Condensed matter

Influence of hybridization on ground-state properties of the Falicov-Kimball model

Pavol Farkašovský

Published Jun 24, 2002• 2 citations
Publisher

Abstract

The density matrix renormalization group and small cluster exact diagonalization calculations are used to examine ground-state properties of the Falicov-Kimball model in one and two dimensions. Particular attention is paid to hybridization effects on insulator-metal transitions. The nature of the ground state is analyzed through the behavior of the single-particle excitation energy and the f and d electron density of states. A number of remarkable results are found. (i) At zero hybridization the gaps in the f and d electron density of states do not coincide, and almost all f electron spectral weight is located outside the d electron subbands. (ii) For nonzero hybridization the f and d electron gaps coincide, for both the symmetric and unsymmetric case. (iii) No insulator-metal transitions driven by hybridization are found in one as well as in two dimensions.

DOI
10.1103/physrevb.65.245119

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The density matrix renormalization group and small cluster exact diagonalization calculations are used to examine ground-state properties of the Falicov-Kimball model in one and two dimensions. Particular attention is paid to hybridization effects on insulator-metal transitions. The nature of the ground state is analyzed through the behavior of the single-particle excitation energy and the f and d electron density of states. A number of remarkable results are found. (i) At zero hybridization the gaps in the f and d electron density of states do not coincide, and almost all f electron spectral weight is located outside the d electron subbands. (ii) For nonzero hybridization the f and d electron gaps coincide, for both the symmetric and unsymmetric case. (iii) No insulator-metal transitions driven by hybridization are found in one as well as in two dimensions.
The density matrix renormalization group and small cluster exact diagonalization calculations are used to examine effects of nonlocal hybridization on ground-state properties of the Falicov-Kimball model in one dimension. Special attention is devoted to the problem of hybridization induced insulator-metal transitions. It is shown that the picture of insulator-metal transitions found for the Falicov-Kimball model with nonlocal hybridization strongly differs from one found for the Falicov-Kimball model without hybridization (as well as with local hybridization). The effect of nonlocal hybridization is so strong that it can induce the insulator-metal transition, even in the half-filled band case where the ground states of the Falicov-Kimball model without hybridization are insulating for all finite Coulomb interactions. Outside the half-filled band case the metal-insulator transition driven by pressure is found for finite values of nonlocal hybridization.
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.
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 density matrix renormalization group method is used to examine possibilities of electronic ferroelectricity in the spinless Falicov-Kimball model. The model is studied for a wide range of parameters including weak and strong interactions as well as the symmetric and unsymmetric case. In all examined cases the 〈d+f〉〈{d}^{+}f〉〈d+f〉-expectation value vanishes for vanishing hybridization V, indicating that the spinless Falicov-Kimball model does not allow for a ferroelectric ground state with a spontaneous polarization.
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.