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Physical review. B, Condensed matter

Application of self-interaction-corrected density-functional formalism to the extended Hubbard model

Yuannan Xie, Rushan Han, Xinwei Zhang

Published Nov 15, 1998• 3 citations
Publisher

Abstract

The density-functional theory for the half-filled extended Hubbard model in one and two dimensions has been studied within the self-interaction-corrected (SIC) local-spin-density (LSD) approximation. The SIC to the total energy is expressed in terms of the Wannier functions which have the most optimal degree of localization. The system at ground state can have spin-density wave (SDW) or charge-density wave (CDW) ordering depending on the relative strength of the on-site repulsion and the nearest-neighbor repulsion. Like the Hartree-Fock approximation, the SIC-LSD scheme predicts a first-order transition between CDW and SDW. However, in the SDW, the nearest-neighbor repulsion V near the transition point tends to increase the band gap for small U and decrease the band gap for large U, with a crossover around $U\ensuremath{\approx}4$ in one dimension, which corresponds to the tricritical point predicted by other theories. The ground-state energies are better described in SIC-LSD than in the Hartree-Fock approximation.

DOI
10.1103/physrevb.58.12721

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The density-functional theory for the half-filled extended Hubbard model in one and two dimensions has been studied within the self-interaction-corrected (SIC) local-spin-density (LSD) approximation. The SIC to the total energy is expressed in terms of the Wannier functions which have the most optimal degree of localization. The system at ground state can have spin-density wave (SDW) or charge-density wave (CDW) ordering depending on the relative strength of the on-site repulsion and the nearest-neighbor repulsion. Like the Hartree-Fock approximation, the SIC-LSD scheme predicts a first-order transition between CDW and SDW. However, in the SDW, the nearest-neighbor repulsion V near the transition point tends to increase the band gap for small U and decrease the band gap for large U, with a crossover around U\ensuremath≈4U\ensuremath{\approx}4U\ensuremath≈4 in one dimension, which corresponds to the tricritical point predicted by other theories. The ground-state energies are better described in SIC-LSD than in the Hartree-Fock approximation.
An efficient minimization method is presented to find the optimal orthogonal localized orbitals within the self-interaction-corrected (SIC) local spin-density (LSD) approximation. By introducing a unified Hamiltonian, both the canonicalvalence bands and conduction bands are obtained by diagonalizing the same matrix. A general criterion for the existence of the self-consistent localized solutions of the SIC-LSD equations is proposed. As an application, we consider the phase diagram and the band structure of the half-filled two-dimensional extended Hubbard model with the next-nearest-neighbor hopping amplitude ${t}^{\ensuremath{'}}.$ The phase boundary between the charge-density wave (CDW) and the spin-density wave (SDW) is determined by comparing the ground-state energies. For nonzero ${t}^{\ensuremath{'}},$ the CDW and SDW states are unstable over a finite portion of the phase diagram at weak coupling.
We show that the self-interaction-corrected (SIC) local spin-density (LSD) approximation can describe localization in a system where the Coulomb interaction is large compared with the band-width. In contrast with the normal LSD approximation, the SIC approximation can be used for a band with orbital degeneracy, even if the band is not half filled. The method is applied to the one-dimensional Hubbard model for which there is an exact solution. The total energy, the band gap, the local moment, and the momentum distribution are substantially better described than in the LSD approximation. For some of these properties the SIC approach is shown to compare favorably with the Gutzwiller ansatz.
The square-lattice extended Hubbard model at half filling is studied by a perturbation scheme. By taking into account the ground state of the mean-field theory as a reference state, the scheme treats the collective fluctuations beyond the mean field as the predominant perturbation. The system at ground state can be a spin-density wave (SDW) or a charge-density wave (CDW) depending on the relative strengths of the on-site electron interaction and the nearest-neighbor interaction. The excitation modes above the ground state are analyzed through diagonalizing an effective Hamiltonian. The energy spectra and the wave functions are self-consistently given by the formalism. By comparing the ground-state energies, we investigate the SDW-CDW transition.
We study the effects of a bond-charge interaction (or correlated hopping) on the properties of the extended [i.e., with both on-site (U) and nearest-neighbor (V) repulsions] Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, X, the charge-density-wave (CDW) state is more robust than the spin-density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when X=0. For X=t and fixed V2t (t is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponds to a different density of doubly occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any X in the range examined. \textcopyright{} 1996 The American Physical Society.
The authors investigate the half-filled Hubbard model in one and two dimensions using approximations to the energy expressed as functionals of the momentum distribution. The functionals are calculated using the Hartree-Fock approximation and density functional theory in the local-spin-density and self-interaction-corrected (SIC) local-spin-density approximations (LSDA) by expressing the ground-state spin densities as a variational ansatz in which the momentum distribution enters as a variational quantity. The autthors calculate the momentum distribution, energy and local moment, as well as their ansatz orbitals, in all three approximations and find that the SIC always improves upon the LSDA.
We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.