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

TitleElectronic excitations: density-functional versus many-body Green's-function approaches
Publication TypePalaiseau Article


Author Address

Onida, G (Reprint Author), Univ Milan, Dept Phys, Ist Nazl Fis Nucl, Via Celoria 16, I-20133 Milan, Italy. Univ Roma Tor Vergata, Dipartimento Fis, Ist Nazl Fis Mat, I-00133 Rome, Italy. Ecole Polytech, CNRS, CEA,UMR 7642, Solides Irradies Lab, F-91128 Palaiseau, France. Univ Pais Vasco, Fac Quim, Dept Fis Mat, Ctr Mixto,CSIC,EHU, San Sebastian 20018, Spain. Donostia Int Phys Ctr, San Sebastian 20018, Spain.

Onida, G, Reining, L, Rubio, A
Year of Publication2002
JournalReviews of Modern Physics

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 1 and the electron-hole interaction. A good approximation for Sigma is obtained with Hedin's G W approach. using density-functional theory as a zero-order solution. First-principles G W 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 Sigma. 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.

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