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Register a new userGW approximation with self-screening correction
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The emph{GW} approximation takes into account electrostatic self-interaction contained in the Hartree potential through the exchange potential. However, it has been known for a long time that the approximation contains self-screening error as evident in the case of the hydrogen atom. When applied to the hydrogen atom, the emph{GW} approximation does not yield the exact result for the electron removal spectra because of the presence of self-screening: the hole left behind is erroneously screened by the only electron in the system which is no longer present. We present a scheme to take into account self-screening and show that the removal of self-screening is equivalent to including exchange diagrams, as far as self-screening is concerned. The scheme is tested on a model hydrogen dimer and it is shown that the scheme yields the exact result to second order in $(U_{0}-U_{1})/2t$ where $U_{0}$ and $U_{1}$ are respectively the onsite and offsite Hubbard interaction parameters and $t$ the hopping parameter.
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We introduce a scheme to include many-body screening processes explicitly into a set of self-consistent equations for electronic structure calculations using the Gutzwiller approximation. The method is illustrated by the application to a tight-binding model describing the strongly correlated {gamma}-Ce system. With the inclusion of the 5d-electrons into the local Gutzwiller projection subspace, the correct input Coulomb repulsion U_{ff} between the 4f-electrons for {gamma}-Ce in the calculations can be pushed far beyond the usual screened value U_{ff}^{scr} and close to the bare atomic value U_{ff}^{bare}. This indicates that the d-f many-body screening is the dominant contribution to the screening of U_{ff} in this system. The method provides a promising way towards the ab initio Gutzwiller density functional theory.
We show that in order to describe the isotropic-nematic transition in stripe forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of two-point correlation function characteristic of a nematic phase.
In many-body perturbation theory (MBPT) the self-energy Sigma=iGWGamma plays the key role since it contains all the many body effects of the system. The exact self-energy is not known; as first approximation one can set the vertex function Gamma to unity which leads to the GW approximation. The latter properly describes the high-density regime, where screening is important; in the low-density regime, instead, other approximations are proposed, such as the T matrix, which describes multiple scattering between two particles. Here we combine the two approaches. Starting from the fundamental equations of MBPT we show how one can derive the T-matrix approximation to the self-energy in a common framework with GW. This allows us to elucidate several aspects of this formulation, including the origin of, and link between, the electron-hole and the particle-particle T matrix, the derivation of a screened T matrix, and the conversion of the T matrix into a vertex correction. The exactly solvable Hubbard molecule is used for illustration.
We present a theoretical framework and implementation details for self-energy embedding theory (SEET) with the GW approximation for the treatment of weakly correlated degrees of freedom and configuration interactions solver for handing the strongly correlated degrees. On a series of molecular examples, for which the exact results are known within a given basis, we demonstrate that SEET(CI/GW) is a systematically improvable and well controlled method capable of giving accurate results and well behaved causal self-energies and Greens functions. We compare the theoretical framework of SEET(CI/GW) to that of GW+DMFT and comment on differences between these to approaches that aim to treat both strongly and weakly correlated simultaneously.
We investigate static correlation and delocalization errors in the self-consistent GW and random-phase approximation (RPA) by studying molecular dissociation of the H_2 and LiH molecules. Although both approximations contain topologically identical diagrams, the non-locality and frequency dependence of the GW self-energy crucially influence the different energy contributions to the total energy as compared to the use of a static local potential in the RPA. The latter leads to significantly larger correlation energies which allow for a better description of static correlation at intermediate bond distances. The substantial error found in GW is further analyzed by comparing spin-restricted and spin-unrestricted calculations. At large but finite nuclear separation their difference gives an estimate of the so-called fractional spin error normally determined only in the dissociation limit. Furthermore, a calculation of the dipole moment of the LiH molecule at dissociation reveals a large delocalization error in GW making the fractional charge error comparable to the RPA. The analyses are supplemented by explicit formulae for the GW Greens function and total energy of a simplified two-level model providing additional insights into the dissociation limit.
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