arXiv:cond-mat/0109479 · Physical review. B, Condensed matter

Falicov-Kimball model and the problem of electronic ferroelectricity

Pavol Farkašovský

Published Jan 30, 2002• 32 citations

Abstract

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 $〈{d}^{+}f〉$-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.

DOI: 10.1103/physrevb.65.081102

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arXiv:cond-mat/0109479 · Physical review. B, Condensed matter

Falicov-Kimball model and the problem of electronic ferroelectricity

Pavol Farkašovský

Published Jan 30, 2002• 32 citations

arXiv HTML PDF

Abstract

〈{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.

DOI: 10.1103/physrevb.65.081102

Related papers

Existence of a ferroelectric ground state with a spontaneous polarization in the Falicov-Kimball model

Pavol Farkašovský

The extrapolation of small-cluster exact-diagonalization calculations is used to examine the possibility of electronic ferroelectricity in the one-dimensional spinless and spin-one-half Falicov-Kimball model (FKM). It is found that neither the spinless nor the spin-one-half version of the FKM allows for a ferroelectric ground state with a spontaneous polarization, i.e., there is no nonvanishing $〈{d}^{+}f〉$ expectation value for vanishing hybridization V.The extrapolation of small-cluster exact-diagonalization calculations is used to examine the possibility of electronic ferroelectricity in the one-dimensional spinless and spin-one-half Falicov-Kimball model (FKM). It is found that neither the spinless nor the spin-one-half version of the FKM allows for a ferroelectric ground state with a spontaneous polarization, i.e., there is no nonvanishing $〈{d}^{+}f〉$ expectation value for vanishing hybridization V.

Physical review. B, Condensed matterApr 15, 199928 citations

Does the Falicov-Kimball model allow for a ferroelectric ground state with a spontaneous polarization?

Pavol Farkašovský

The extrapolation of small-cluster exact-diagonalization calculations is used to examine the possibility of electronic ferroelectricity in the one dimensional spinless and spin-one-half Falicov-Kimball model (FKM). It is found that neither spinless nor spin-one-half version of the FKM does not allow for a ferroelectric ground state with a spontaneous polarization, i.e. there is no nonvanishing $$-expectation value for vanishing hybridization $V$ .The extrapolation of small-cluster exact-diagonalization calculations is used to examine the possibility of electronic ferroelectricity in the one dimensional spinless and spin-one-half Falicov-Kimball model (FKM). It is found that neither spinless nor spin-one-half version of the FKM does not allow for a ferroelectric ground state with a spontaneous polarization, i.e. there is no nonvanishing $$-expectation value for vanishing hybridization $V$.

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L. G. Sarasúa, M. A. Contínentino

We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension $(d=1).$ Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions $〈{\mathrm{cf}}^{+}〉$ are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension $(d=1).$ Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions $〈{\mathrm{cf}}^{+}〉$ are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.

Physical review. B, Condensed matterJun 20, 200215 citations

〈{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.

〈{d}^{+}f〉

expectation value for vanishing hybridization V.

V

We obtain exact ground states for the spinless Falicov-Kimball model with hybridization in one dimension

(d=1).

Ground-state energies and their corresponding wave functions are given for a restricted region of the parameter space in the limit of strong interactions for the half-filling condition. We find that the ground states possess a diagonal long range order and constitute a condensation of excitons in a zero momentum state. On the other hand, the correlation function $A=〈{d}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{f}_{i}〉$ is purely imaginary, indicating that the ground state does not exhibit spontaneous ferroelectricity.

(a/t,h)

plane, where

a/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.

We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension

(d=1).

Ground-state energies and their corresponding wave functions are obtained for a restricted region of the parameter space of the model Hamiltonian. In particular, two ground states are obtained, one containing one electron per site and the other three electrons per site. The expectation values of the occupation numbers and of the excitonic correlation functions

〈{\mathrm{cf}}^{+}〉

are calculated using the exact ground state wave functions. Finally we discuss the possibility of a ferroelectric ground state in the Falicov-Kimball model.