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Physical Review B

Self-consistent projection operator approach to excitation spectra: Role of correlated wave function

Y. Kakehashi, Peter Fulde

Published Oct 27, 2004• 3 citations
Publisher

Abstract

A recently proposed combination of a projection operator method with the coherent potential approximation for the computation of the excitation spectra of solids is further extended. In particular, the effect of electron correlations on the matrix elements of the self-energy are investigated. This is done with the help of a Gutzwiller-type variational wave function. Numerical calculations have been performed for a half-filled band of a hypercubic lattice in infinite dimensions. They show that for strong electron correlations the higher-order dynamical corrections in an renormalized perturbation expansion are screened except in the low-energy regime. This provides for a justification of earlier work, where a Hartree-Fock approximation with a cutoff parameter was used for the computation of the static matrix elements.

DOI
10.1103/physrevb.70.155112

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Journal of Physics Conference Series•Dec 14, 2012•0 citations
A recently proposed combination of a projection operator method with the coherent potential approximation for the computation of the excitation spectra of solids is further extended. In particular, the effect of electron correlations on the matrix elements of the self-energy are investigated. This is done with the help of a Gutzwiller-type variational wave function. Numerical calculations have been performed for a half-filled band of a hypercubic lattice in infinite dimensions. They show that for strong electron correlations the higher-order dynamical corrections in an renormalized perturbation expansion are screened except in the low-energy regime. This provides for a justification of earlier work, where a Hartree-Fock approximation with a cutoff parameter was used for the computation of the static matrix elements.
A theory of the single-particle excitation spectrum is presented on the basis of the projection operator method combined with the many-body coherent-potential approximation (CPA). The theory describes the dynamics of the excitations by means of an energy-dependent Liouville operator accompanied by a coherent potential which is determined by the self-consistent CPA condition. It is shown that the present theory is essentially equivalent to the dynamical CPA and the dynamical mean-field theory. The Hubbard III approximation and the modified perturbation theory are rederived from the theory. A renormalized perturbation scheme for the Green function is developed on the basis of a general formula for the memory function. It interpolates between the weak- and strong-Coulomb interaction limits, and yields the metal-insulator transition for half-filled bands. Numerical calculations have been performed for the Gutzwiller-Hubbard model on a hypercubic lattice in infinite dimensions. The results show that the theory describes quantitatively the quasiparticle weight vs Coulomb interaction curve, yielding a reasonable critical Coulomb interaction for the metal-insulator transition. It produces the overall features of the excitation spectra and the momentum distributions for various Coulomb interaction strengths.
A self-consistent projection operator method for single-particle excitations is developed. It describes the nonlocal correlations on the basis of a projection technique to the retarded Green function and the off-diagonal effective medium. The theory takes into account long-range intersite correlations making use of an incremental cluster expansion in the medium. A generalized self-consistent coherent potential is derived. It yields the momentum-dependent excitation spectra with high resolution. Numerical studies for the Hubbard model on a simple cubic lattice at half filling show that the theory is applicable in a wide range of Coulomb interaction strength. In particular, it is found that the long-range antiferromagnetic correlations in the strong interaction regime cause shadow bands in the low-energy region and sub-peaks of the Mott–Hubbard bands.
We extend the projection operator method combined with the coherent potential approximation (CPA) to the nonlocal case in order to describe the momentum dependence of the single-particle self-energy. The inter-site excitations are taken into account successively by means of an incremental cluster expansion. The cluster memory functions embedded in a medium are obtained by extending a renormalized perturbation scheme. The medium is self-consistently determined from a CPA condition. In the weak Coulomb interaction limit the self-energy reduces to the second-order perturbation theory, but it is also correct in the atomic limit. Numerical calculations are performed for a Hubbard model at half filling on a simple-cubic lattice. It is demonstrated that the kkk-dependent self-energy reduces the quasiparticle density of states at the Fermi level, and broadens the band. Furthermore, in the metallic region it produces well-defined satellite bands around the $\ensuremath{\Gamma}$ and R points in the Brillouin zone. The momentum-dependent effective mass and the momentum distribution are also presented. The critical Coulomb interaction for the divergence of the effective mass is estimated to be at least twice as large as the one obtained in the single-site approximation.
A self-consistent projection operator method for single-particle excitations is developed. It describes the nonlocal correlations on the basis of a projection technique to the retarded Green function and the off-diagonal effective medium. The theory takes into account long-range intersite correlations making use of an incremental cluster expansion in the medium. A generalized self-consistent coherent potential is derived. It yields the momentum-dependent excitation spectra with high resolution. Numerical studies for the Hubbard model on a simple cubic lattice at half filling show that the theory is applicable in a wide range of Coulomb interaction strength. In particular, it is found that the long-range antiferromagnetic correlations in the strong interaction regime cause shadow bands in the low-energy region and sub-peaks of the Mott-Hubbard bands.
A new wavefunction which improves the Gutzwiller-type local ansatz method has been proposed to describe the correlated electron system. The ground-state energy, double occupation number, momentum distribution function, and quasiparticle weight have been calculated for the half-filled band Hubbard model in infinite dimensions. It is shown that the new wavefunction improves the local-ansatz approach (LA) proposed by Stollhoff and Fulde. Especially, calculated momentum distribution functions show a reasonable momentum dependence. The result qualitatively differs from those obtained by the LA and the Gutzwiller wavefunction. Furthermore, the present approach combined with the projection operator method CPA is shown to describe quantitatively the excitation spectra in the insulator regime as well as the critical Coulomb interactions for a gap formation in infinite dimensions.
We present here the momentum dependent local-ansatz wavefunction approach (MLA) with the best choice of the self-consistent variational parameters to describe the ground-state properties of the correlated electron systems in solids. With use of the self-consistent variational scheme, we performed the numerical calculations for the half-filled band as well as non-half-filled band Hubbard model on the hypercubic lattice in infinite dimensions. The ground-state energy in the MLA is lower than those of the local-ansatz approach (LA) and the Gutzwiller approach (GA) in weak and intermediate Coulomb interaction regimes. The double occupation number is suppressed as compared with the LA. We observe the distinct momentum dependence of the momentum distribution functions which is qualitatively different from those of the LA and the GA.