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Physical review. B, Condensed matter

Exact results for the extended Anderson model with Falicov-Kimball interactions

L. G. Sarasúa, M. A. Contínentino

Published Jun 20, 2002• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.65.233107

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We present exact results for the extended periodic Anderson model with Falicov-Kimball interactions in one dimension (d=1).(d=1).(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 〈cf+〉〈{\mathrm{cf}}^{+}〉〈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 obtain exact ground states for the spinless Falicov-Kimball model with hybridization in one dimension (d=1).(d=1).(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.
Ground-state properties of the asymmetric Hubbard model are studied on one-dimensional clusters (rings) with N=6, 8, and 10 sites. The ground-state energy, correlation functions, and phase diagrams are determined for various sets of model parameters. Computations are performed both by exact diagonalization (for N=6) and by an approximate method by which correlation effects can be examined on larger clusters than exact diagonalization allows. In the limiting cases (one limit corresponds to the spinless Falicov-Kimball model and the other to the Hubbard model) our results agree quite well with those obtained analytically for infinite systems.
The extended Falicov-Kimball model is analyzed exactly in the ground state at half filling in the limit of large dimensions. In the model the on-site and the intersite density-density interactions between all particles are included. We determined the model's phase diagram and found a discontinuous transition between two different charge-ordered phases. Our analytical calculations show that the ground state of the system is insulating for any nonzero values of the interaction couplings. We also show that the dynamical mean-field theory and the static broken-symmetry Hartree-Fock mean-field approximation give the same results for the model at zero temperature. In addition, we prove using analytical expressions that at infinitesimally small, but finite, temperatures the system can be metallic.