With the eigenfunctional theory, we study a general interacting electron system, and give a rigorous expression of its ground state energy which is composed of two parts, one part is contributed by the non-interacting electrons, and another one is represented by the correlation functions that are controlled by the electron correlation. Moreover, according to the rigorous expression of the ground state energy, an effective method beyond the local density approximation of the density functional theory is proposed.
With the eigenfunctional theory, we study a general interacting electron system, and give a rigorous expression of its ground state energy, which is composed of two parts: one part is contributed by the non-interacting electrons, and the other one is represented by the correlation functions that are controlled by the electron correlation. Moreover, according to the rigorous expression of the ground state energy, an effective scheme beyond the local density approximation of the density functional theory is proposed. As a simple example for a spin-1/2 XXZ chain, under the linear approximation in solving the equation of the phase field, the ground state energy obtained by the present scheme is quite close to that of the Bethe ansatz.
Beyond the usual many body perturbation theory, with the eigenfunctional theory, we directly calculate the correlation function produced by the Coulomb interaction of electrons in the equation of one-electron Green function, and give the general expression of the non-local effective interaction potential in a Hartree-type potential, which is absent in all previous many body perturbation theories. This effective interaction potential originates from the quantum many body effect of the system, and it cannot be obtained directly by the usual perturbation expression approach. Moreover, using theoretical models, we demonstrate that this effective interaction potential can be used to characterize the electron correlation strength of the system.
We introduce a scheme through which the ground-state electronic density n and total energy Ey[n] of inhomogeneous interacting systems can be determined in a self-consistent (SC) way. It is based on a SC perturbation expansion for the single-particle Green function G. Our employed expansion is argued to be valid under all conditions provided that the ground-state charge density of the interacting system is pure-state non-interacting v representable. The formalism discussed in this paper has been applied to a quasi-one-dimensional periodic system. It has even been possible to carry out SC calculations with the dynamically screened exchange diagram (the so-called G W diagram, where W is the dynamically screened electron4ectron interaction function) for the selfenergy operator C. A coherent mode of interpretation of a number of our results entails that the overwhelming success of the G W framework in relatively accurately reproducing the experimental energy gaps of a number of semiconductors and insulators may be a direct consequence of non-selfconsistency effects; whereas a non-self-consistent calculation in our tests increases the value of the local-density approximation (LDA) gap in the range of 40-65% of the ‘experimental’ gaps, self-consistency effects reduce this range to 1 4 1 7 % . The same line of argument leads us to conclude that, in our model, 2635% of the LDA error in the gap energies is due to the absence of a well known discontinuity in the LDA exchange-correlation potential, and the remaining part is due to the Kohn-Sham eigenvalues not being identifiable with one-particle excitation energies. A natural conclusion that may be drawn from these observations is that a correct description of excitation energies (e.g. of the gap energy) cannot be achieved without including, at least approximately, the vertex part of C, which is entirely absent in the GW scheme. 5 1 . INTRODUCTION The ground-state (GS) density-functional theory (DFT) due to Hohenberg and Kohn (1964) provides a rigorous foundation for determining properties of systems in their ground states (for reviews see Lundqvist and March (1983), Jones and Gunnarsson (1989) and Dreizler and Gross (1990)). The central position in this theory is taken by the total-energy functional EY[n] which, owing to its unique absolute minimum a t the GS electronic density n, can be used to obtain not only the GS energy but also the GS charge density. tPresent address: Max-Planck-Institut fur Festkorperforschung, HeisenbergstraRe 1, 70569 Stuttgart, Federal Republic of Germany. 0141-8637/97 $12 .00
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed, thus transforming exactly, in a physically transparent way, an important part of the electron-electron interaction into an effective local one-body potential. We test our approach on quasi-one-dimensional systems, showing that it captures essential features of strong correlation that restricted Kohn-Sham calculations using the currently available approximations cannot describe.
We present a rigorous formulation of generalized Kohn-Sham density-functional theory. This provides a straightforward Kohn-Sham description of many-body systems based not only on particle-density but also on any other observable. We illustrate the formalism for the case of a particle-density based description of a nonrelativistic many-electron system. We obtain a simple diagrammatic expansion of the exchange-correlation functional in terms of Kohn-Sham single-particle orbitals and energies; develop systematic Kohn-Sham formulation for one-electron propagators and many-body excitation energies. This work is ideally suited for practical applications and provides a rigorous basis for a systematic development of the existing body of first-principles calculations in a controllable fashion.
In this paper, we present the rigorous expression of the ground state energy and study the phase transition of the three-dimensional homogeneous electron gas by the eigenfunctional theory. The ground state energy is decided completely by the pair distribution function $ g(r)$, which is, by definition, strictly a positive function. But when the density decreases, the electronic correction effect becomes strong from weak, the previous theories basing on one-particle approximation, such as: RPA, Hubbard and STLS ,\cite{4,9} can't insure
g(r) positive always, which implies that they are becoming invalid and overestimate the ground state energy. The eigenfunctional theory has a significant improvement over them, under the linear approximation in solving the equation of the phase field, the
g(r) obtained by the eigenfunctional theory is always positive and can well satisfy the normalization integral (
n0∫d3r[g(r)−1]=−1) which is one of the important features of
g(r). After obtaining
g(r) and calculating the ground state energy of the electron gas both in paramagnetic and ferromagnetic by
g(r), we observe a continuous phase transition from paramagnetic to the ferromagnetic occurring at
rs=19.9±0.8. This can be indirectly supported by the observation of a ferromagnetic state in doped hexaboride
(Ca1−xLaxBb),\cite{42} and is close to the result of G.Ortiz et.al (
rs=20±5).\cite{12}