@article{18617, abstract = {{The decay properties of the one-particle Green function in real space and imaginary time are systematically studied for solids. I present an analytic solution for the homogeneous electron gas at finite and at zero temperature as well as asymptotic formulas for real metals and insulators that allow an analytic treatment in electronic-structure calculations based on a space-time representation. The generic dependence of the decay constants on known system parameters is used to compare the scaling of reciprocal-space algorithms for the GW approximation and the space-time method.}}, author = {{Schindlmayr, Arno}}, issn = {{1095-3795}}, journal = {{Physical Review B}}, number = {{19}}, pages = {{12573--12576}}, publisher = {{American Physical Society}}, title = {{{Decay properties of the one-particle Green function in real space and imaginary time}}}, doi = {{10.1103/PhysRevB.62.12573}}, volume = {{62}}, year = {{2000}}, } @article{18619, author = {{Schindlmayr, Arno}}, issn = {{1943-2909}}, journal = {{American Journal of Physics}}, number = {{10}}, pages = {{933--934}}, publisher = {{American Institute of Physics}}, title = {{{Universality of the Hohenberg–Kohn functional}}}, doi = {{10.1119/1.19156}}, volume = {{67}}, year = {{1999}}, } @article{18620, abstract = {{With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GW approximation with those from an extended GWΓ scheme that includes a nontrivial vertex function and the fundamentally distinct Bethe-Goldstone approach based on the T matrix. The self-consistent Green’s function G, as derived from Dyson’s equation, is used not only in the self-energy but also to construct the screened interaction W for a model system. For all approximations we observe a similar deterioration of the spectrum, which is not removed by vertex corrections. In particular, satellite peaks are systematically broadened and move closer to the chemical potential. The corresponding total energies are universally raised, independent of the system parameters. Our results, therefore, suggest that any improvement in total energy due to self-consistency, such as for the electron gas in the GW approximation, may be fortuitous.}}, author = {{Schindlmayr, Arno and Pollehn, Thomas Joachim and Godby, Rex William}}, issn = {{1095-3795}}, journal = {{Physical Review B}}, number = {{19}}, pages = {{12684--12690}}, publisher = {{American Physical Society}}, title = {{{Spectra and total energies from self-consistent many-body perturbation theory}}}, doi = {{10.1103/PhysRevB.58.12684}}, volume = {{58}}, year = {{1998}}, } @article{18622, abstract = {{We present a general procedure for obtaining progressively more accurate functional expressions for the electron self-energy by iterative solution of Hedin's coupled equations. The iterative process starting from Hartree theory, which gives rise to the GW approximation, is continued further, and an explicit formula for the vertex function from the second full cycle is given. Calculated excitation energies for a Hubbard Hamiltonian demonstrate the convergence of the iterative process and provide further strong justification for the GW approximation.}}, author = {{Schindlmayr, Arno and Godby, Rex William}}, issn = {{1079-7114}}, journal = {{Physical Review Letters}}, number = {{8}}, pages = {{1702--1705}}, publisher = {{American Physical Society}}, title = {{{Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation}}}, doi = {{10.1103/PhysRevLett.80.1702}}, volume = {{80}}, year = {{1998}}, } @article{18624, abstract = {{We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show how a proper treatment can improve computational implementations of many-body perturbation theory in general. Exchange-only and GW calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable.}}, author = {{Pollehn, Thomas Joachim and Schindlmayr, Arno and Godby, Rex William}}, issn = {{1361-648X}}, journal = {{Journal of Physics: Condensed Matter}}, number = {{6}}, pages = {{1273--1283}}, publisher = {{IOP Publishing}}, title = {{{Assessment of the GW approximation using Hubbard chains}}}, doi = {{10.1088/0953-8984/10/6/011}}, volume = {{10}}, year = {{1998}}, } @article{18626, abstract = {{We present a simple analytic scheme for calculating the binding energy of excitons in semiconductors that takes full account of the existing anisotropy in the effective mass, as a complement to the qualitative treatment in most textbooks. Results obtained for excitons in gallium nitride form the basis for a discussion of the accuracy of this approach.}}, author = {{Schindlmayr, Arno}}, issn = {{1361-6404}}, journal = {{European Journal of Physics}}, number = {{5}}, pages = {{374--376}}, publisher = {{IOP Publishing and The European Physical Society}}, title = {{{Excitons with anisotropic effective mass}}}, doi = {{10.1088/0143-0807/18/5/011}}, volume = {{18}}, year = {{1997}}, } @article{18628, abstract = {{We present a nontrivial model system of interacting electrons that can be solved analytically in the GW approximation. We obtain the particle number from the GW Green’s function strictly analytically, and prove that there is a genuine violation of particle number conservation if the self-energy is calculated non-self-consistently from a zeroth order Green’s function, as done in virtually all practical implementations. We also show that a simple shift of the self-energy that partially restores self-consistency reduces the numerical deviation significantly.}}, author = {{Schindlmayr, Arno}}, issn = {{1095-3795}}, journal = {{Physical Review B}}, number = {{7}}, pages = {{3528--3531}}, publisher = {{American Physical Society}}, title = {{{Violation of particle number conservation in the GW approximation}}}, doi = {{10.1103/PhysRevB.56.3528}}, volume = {{56}}, year = {{1997}}, } @article{18630, abstract = {{Inspired by earlier work on the band-gap problem in insulators, we reexamine the treatment of strongly correlated Hubbard-type models within density-functional theory. In contrast to previous studies, the density is fully parametrized by occupation numbers and overlap of orbitals centered at neighboring atomic sites, as is the local potential by the hopping matrix. This corresponds to a good formal agreement between density-functional theory in real space and second quantization. It is shown that density-functional theory is formally applicable to such systems and the theoretical framework is provided. The question of noninteracting v representability is studied numerically for finite one-dimnsional clusters, for which exact results are available, and qualitatively for infinite systems. This leads to the conclusion that the electron density corresponding to interacting systems of the type studied here is in fact not noninteracting v representable because the Kohn-Sham electrons are unable to reproduce the correlation-induced localization correctly.}}, author = {{Schindlmayr, Arno and Godby, Rex William}}, issn = {{1095-3795}}, journal = {{Physical Review B}}, number = {{16}}, pages = {{10427--10435}}, publisher = {{American Physical Society}}, title = {{{Density-functional theory and the v-representability problem for model strongly correlated electron systems}}}, doi = {{10.1103/PhysRevB.51.10427}}, volume = {{51}}, year = {{1995}}, }