Dynamical aspects of correlation corrections in a covalent crystal

Strinati, G. C.; Mattausch, Hj.; Hanke, W.

doi:10.1103/physrevb.25.2867

Cited by 291 publications

(147 citation statements)

References 83 publications

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“…Quasiparticle damping times were calculated for diamond by Strinati et al (1980Strinati et al ( , 1982, who found results consistent with photoemission data. A treatment of the electron dynamics, including band structure and dynamical screening effects, is necessary for quantitative comparisons with experiment (see, for instance, Bü rgi et al, 1999;Valla et al, 1999b).…”

Section: A Evaluation Of the Green's Function Gmentioning

confidence: 71%

Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress. CONTENTS

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Section: A Evaluation Of the Green's Function Gmentioning

confidence: 71%

Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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“…Thereby the problem of double counting of the interactions must be carefully considered. More recently the LDA+U has been combined with the dynamical mean-field theory (DMFT) 5 , an extension of the coherent potential approximation (CPA) to include the effects of dynamical fluctuations (dynamical CPA) 6 , or the so-called GW method 7,8 .…”

Section: Introductionmentioning

confidence: 99%

A Simplified Method for the Computation of Correlation Effects on the Band Structure of Semiconductors

2006

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We present a simplified computational scheme in order to calculate the effects of electron correlations on the energy bands of diamond and silicon. By adopting a quasiparticle picture we compute first the relaxation and polarization effects around an electron set into a conduction band Wannier orbital. This is done by allowing the valence orbitals to relax within a self-consistent field (SCF) calculation. The diagonal matrix element of the Hamiltonian leads to a shift of the center of gravity of the conduction band while the off-diagonal matrix elements result in a small reduction of the conduction-electron band width. This calculation is supplemented by the computation of the loss of ground state correlations due to the blocked Wannier orbital into which the added electron has been placed. The same procedure applies to the removal of an electron, i.e., to the valence bands. But the latter have been calculated previously in some detail and previous results are used in order to estimate the energy gap in the two materials. The numerical data reported here shows that the methods works, in principle, but that also some extension of the scheme is necessary to obtain fully satisfactory results.Dedicated to J.-P. Malrieu on the occasion of his 60th birthday.

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“…We also investigate the smallest value of R max which is needed to obtain accurate results for each value of L. This allows us to obtain fully self consistent results, independent of the starting point where local density approximation (LDA) to density functional theory (DFT) [15] serves in many cases [6,7,8,9]. We establish that even in the case of semiconductors when the Coulomb interactions have an infinite range due to lack of screening, a reasonable small cluster produces very accurate results.…”

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confidence: 99%

“…Keeping R max = ∞ and n = 1 corresponds to the famous GW approximation [3,6,7,8,9]. R max = 1 and n max = 1 is reduced to the local GW approximation introduced by Zein and Antropov [10], as an approximation to accelerate the convergence of the GW method.…”

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confidence: 99%

Local Self-Energy Approach for Electronic Structure Calculations

Ne¹,

Sy²,

Kotliar³

2006

Phys. Rev. Lett.

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Using a novel self-consistent implementation of Hedin's GW perturbation theory we calculate space and energy dependent self-energy for a number of materials. We find it to be local in real space and rapidly convergent on second-to third-nearest neighbors. Corrections beyond GW are evaluated and shown to be completely localized within a single unit cell. This can be viewed as a fully self consistent implementation of the dynamical mean field theory for electronic structure calculations of real solids using a perturbative impurity solver.PACS numbers: PACS numbers: 71.28.+d, 71.25.Pi, 75.30.Mb The construction of a controlled practical approximation to the many body problem of solid state physics is a long sought goal. Controlled approximations are important because the accuracy of the results can be improved in a systematic way. This goal has been achieved in quantum chemistry by the configuration interaction (CI) method. CI can be thought as a controlled approximation that becomes more accurate as two factors are increased: a) the number of configurations (i.e. Slater determinants) kept and b) the size of the basis used to represent the one-particle orbitals which are used to represent the configurations. Dynamical mean field theory (DMFT) and its cluster extensions (C-DMFT) [1][2] merge CI ideas with band structure methods. They allow us to tackle the problem of periodic infinite systems.The central goal is the computation of the one-electron Greens function, (its Fourier transform can be measured via photoemission and inverse photoemission spectroscopy), G(r, r ′ , ω), and the self-energy Σ(r, r ′ , ω). The interaction functional Φ[G, W ] is then expanded in a perturbative series. The first few graphs are shown in Fig 1(a) and corresponds to the Hartree, the GW, and the first correction beyond GW. Variations of Φ over G and W give us Σ and Π. For the self-energy these diagrams are given in Fig 1(b). To solve the corresponding Dyson equations numerically one introduces a basis set and corresponding expansions for the self energies polar- izations and effective interactions. Cluster DMFT ideas truncate the functional Φ, Σ and Π by setting its variables, i.e. the Greens functions, equal to zero beyond a given range R. When R is one lattice spacing we have the highly successful single site DMFT, as the range R increases the approximation converges to the solution of the full many-body problem. In this paper we address the central problem of determining the minimal range that is needed to obtain accurate results for various materials.There are three different parameters that need to be increased to achieve convergence, a) the size of the basis set L max , b) the order of the perturbation theory kept n max , c) the range of the graphs R max which needs to be kept to obtain accurate approximation. R max depends on L and n. We do not consider in this paper the important issue of convergence as a function of L max as well as the dependence of the range of the type of basis set chosen. Instead we make the choice of a...

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Dynamical aspects of correlation corrections in a covalent crystal

Cited by 291 publications

References 83 publications

Electronic excitations: density-functional versus many-body Green’s-function approaches

Electronic excitations: density-functional versus many-body Green’s-function approaches

A Simplified Method for the Computation of Correlation Effects on the Band Structure of Semiconductors

Local Self-Energy Approach for Electronic Structure Calculations

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