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Invited Talks

Orbital degeneracy and Mott transition: "Fixed node" lattice Monte-Carlo calculations for a C60 model

O. Gunnarsson
Max-Planck-Institut für Festkörperforschung,
D-70506 Stuttgart, Germany

E. Koch and R.M. Martin
Department of Physics, University of Illinois, Urbana, Illinois 61801

For doped C60 compounds, U/W is estimated to be 1.5-2.5, where U is the on-site Coulomb interaction and W is the one-particle band width. Since the criterion for a Mott-Hubbard metal-insulator transition is believed to be U/W~1, it has been suggested that stoichiometric A3C60 (A=K, Rb) must be Mott-Hubbard insulators. We argue that the condition for a Mott transition in a half-filled Hubbard model with the orbital degeneracy N is U/W~sqrt(N). These conclusions are supported by exact diagonalization calculations for small systems and lattice "fixed-node" diffusion Monte Carlo calculations for larger systems. For a Hubbard model with a three-fold orbital degeneracy our Monte-Carlo calculations give a critical ratio Uc/W~2.5. This should then put A3C60 on the metallic side of a Mott-Hubbard transition.

Hartree-Fock description of NiO: a starting point for correlated procedures?

University of St.Andrews

It is a widely held view that NiO and similiar materials are strongly correlated systems. If this is true, it might reasonably be concluded that single-particle descriptions such as Hartree- Fock are unable to account for their more important properties. This talk will present the results of recent ab initio periodic Hartree-Fock calculations of the electronic structure, magnetism and hole states in NiO (and other systems if time permits) which suggest that the above conclusion might need to be reconsidered and that the Hartree-Fock wave function could provide a very useful starting point for more exact treatments.

Contributed Papers

Exchange and Correlation holes in jellium surfaces

Paulo H. Acioli

Departamento de Fisica, Universidade de Brasilia, Brasilia, DF, 70.910, Brazil (e-mail: pacioli@helium.fis.unb.br)

David M. Ceperley

National Center for Supercomputing Applications, Physics Department, University of Illinois at Urbana-Champaign, Urbana, IL 61.801, USA

The understanding of correlation effects in inhomogeneous systems can provide useful information to improve current approximations of density functional theory. The jellium model of a surface is a prototype of inhomogeneous systems. We present the results of fixed-node diffusion Monte Carlo calculations of jellium surfaces for metallic densities. The surface energies agree with results obtained using the Langreth-Mehl and Perdew-Wang (91) generalized gradient approximations at high densities (rs less than 2.7). At low densities (rs greater than 3.25) they agree with Fermi-hyppernetted-chain calculations. We computed and tabulated the pair correlation functions near the surface and show the anisotropic character of the exchange-correlation hole in regions of fast- varying density.

Multiple plasmon satellites in Na and Al spectral functions from cumulant expansion

F. Aryasetiawan 1,2, L. Hedin 1, and K. Karlsson 3

1 Max-Planck-Institut fuer Festkoerperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany

2 Department of Theoretical Physics, University of Lund, Soelvegatan 14A, S-223 62 Lund, Sweden

3 Department of Engineering Science, Hoegskolan i Skoevde, 54128 Skoevde, Sweden

The valence photoemission spectra of alkali metals exhibit multiple plasmon satellite structure. The calculated spectral functions within the GW approximation show only one plasmon satellite at too large binding energy. In this work we use the cumulant expansion approach to obtain the spectral functions of Na and Al from ab initio calculations including the effects of bandstructure. The GW spectral functions are dramatically improved and the positions of the multiple plasmon satellites are in very good agreement with experiment while their intensities cannot be explained from intrinsic effects only.

A quantum Monte Carlo approach to exchange-correlation of the inhomogeneous electron gas

M. Nekovee and W.M.C. Foulkes

Imperial College, Prince Consort Road, London SW7 2BZ, UK

G. Rajagopal, A. Williamson and R.J. Needs

University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK

The exchange-correlation energy functional Exc plays a fundamental role in the density functional theory of interacting electron systems. Using an adiabatic connection between the non-interacting electron system and the fully interacting system, Exc can be expressed in terms of the non-local exchange-correlation hole surrounding each electron. We devised a new method for evaluating the exchange-correlation hole of the inhomogeneous electron gas which is based on combining the above adiabatic connection with accurate variational quantum Monte Carlo calculations. We discuss aspects of the method and illustrate it with a first application to an inhomogeneous electron system.

Assessment of further many-body approximations using 1D and 2D Hubbard model systems

T. Pollehn (1), R.W. Godby (2)

(1) TCM Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK

(2) Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom

The frameworks of GW- or ladder ("T-Matrix") approximations allow for a number of variations on how to obtain a spectral function: Different Hamiltonians can be chosen to start the iteration, various screened Coulomb interactions can be used, and there are a number of further numerical details that allow for a whole host of different approximations.

It is the aim of our work to compare the results of these techniques with exact spectral functions to enable us to set up a list of criteria on how to choose an appropriate approximation for a given system. In order to come to general conclusions we explore a range of systems, using different dimensions, band fillings and correlation strengths.

The exact results necessary for our work are only at hand for small model systems. We will however show how to diagonalise comparatively large Hamiltonians (matrices of order 100,000) exactly, and how to use this information to gain confidence that the findings will remain true if still larger systems (for which exact results are no longer at hand) are considered.

The charge density of semiconductor heterostructures with the GW space-time method

M. M. Rieger(1), R.W. Godby(2), H.N. Rojas(1,3), and R.J. Needs(1)

(1) Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK

(2) Department of Physics, University of York, Heslington, York YO1 5DD, UK

(3) Permanent address: Universidad Privada Boliviana, Cochabamba, Bolivia

We present a new method for calculating the electronic charge density of periodic semiconductor structures based on the GW approximation. This makes it possible for the first time to choose the Hartree potential consistent with the GW approximation.

At the heart of the calculations is the GW space-time method. In this method the Green function, the screened Coulomb interaction, the polarisability and the self-energy are represented on a real-space grid and along the imaginary energy axis. Where necessary, fast Fourier transforms provide for efficient changes between representations. The computational effort in this method scales quadratically both with regard to the number of Fourier coefficients of the input LDA wavefunctions and with regard to cell size, as opposed to the fourth-power scaling of reciprocal-space computations.

These efficiency gains, together with the added advantages of relative smoothness and rapid convergence of the quantities on the imaginary time or energy axis, as opposed to the real axis, enable us to calculate the full self-energy at the GW/RPA level, without recourse to plasmon-pole models for the energy dependence. By means of the Dyson equation we are then able to extract a correction to the LDA Green function and eventually the charge density. The changes in the Hartree potential are taken account of in a self-consistent cycle.

Results for elemental group IV semiconductors and SiGe superlattices will be presented.

Quasiparticle energies of bulk and surface core levels

Michael Rohlfing, Peter Krüger, and Johannes Pollmann

Institut für Theoretische Physik II, Universität Münster, D-48149 Münster, Germany

In this paper we address the binding energies of core electrons (e.g., Cd 4d, Ge 3d, Si 2p) in semiconductors within LDA and within GW quasiparticle calculations. We have developed a method for evaluating the GWA using basis sets of localized Gaussian orbitals. This enables us to apply the GWA to the strongly localized core states with very modest effort.

It is well-known that the LDA systematically underestimates the binding energies of core states by up to 20 percent. By the quasiparticle (QP) corrections resulting from a conventional GW calculation, the binding energies are increased but are still too small if compared with experiment. We show that the binding energies are increased further by employing a self-consistent GW self-energy operator. For the calculation of this self-energy operator one has to employ the resulting QP energies instead of the LDA spectrum. Furthermore, we renormalize the QP amplitudes and take satellite structures into account, which again increases the binding energies of the core states. Our final results for the QP binding energies of the core states Si 2p in Si, Ge 3d in Ge and Cd 4d in CdS are in good agreement with available experimental data.

At surfaces, the core levels of the substrate atoms are shifted due to the chemical environment that is different from the bulk. Our approach allows for a direct calculation of these shifts within LDA and within GWA. As an example, we present surface core-level shifts of clean and adsorbate-covered Si surfaces.

Iterative solution of Hedin's equations beyond the GW approximation

Arno Schindlmayr1 and R. W. Godby2

1 Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom
2 Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom

Many-body theory allows the description of electronic systems in terms of the Green's function G, which is rigorously defined through the many-body wave function but of more accessible analytic form. In practice, approximate Green's functions are derived using Dyson's equation and a system of self-consistent integral equations known as Hedin's equations that relate G to other macroscopic quantities such as the self-energy, the screened Coulomb interaction W, the polarisation propagator, and a vertex function. While the GW approximation to the self-energy, which has been used to great success in a wide variety of different systems, is derived in first iteration of this system of integral equations starting from Hartree theory, analytic difficulties have so far prevented a further iterative solution beyond this first approximation. In this work we present the expression for the second-iteration vertex function in closed analytic form as well as first results for a two-dimensional Hubbard model obtained within this framework.

Ab-initio many-body calculations with the space-time GW method on a parallel computer

L. Steinbeck1, W.G. Aulbur2, R.W. Godby1 and M.M. Rieger3

1 Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom

2 Department of Physics, Ohio State University, 174 W. 18th Avenue, Columbus, OH 43210-1106, USA

3 Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom

Recently, a real-space imaginary-time method for ab-initio many-body calculations for solids within the GW approximation has been developed where Green function, polarizability, screened Coulomb interaction, and electron self-energy are represented on a real-space grid and on the imaginary time axis. Changes between real and reciprocal space representations are efficiently done by fast Fourier transformation. The method allows to calculate the full GW self-energy without resorting to any model form of the screened Coulomb interaction and exhibits a more favourable scaling of the computational effort with system size than reciprocal-space methods. As the method is based on real-space representation and fast Fourier transforms it is suited for parallelization.

The space-time GW code has been parallelized using a message-passing interface parallelization scheme to run on a parallel computer. This allows more complex systems to be studied such as semiconductor materials with large unit cells or transition metals. We discuss various aspects of the parallelization such as the parallelization concept, performance issues, potential applications, and problems and present preliminary results.

Lowest order vertex- and selfconsistency-corrections to RPA-GW

R.T.M. Ummels, H.J. de Groot, P.A. Bobbert, W. van Haeringen

Dept. of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands

State-of-the-art GW selfenergy-calculations neglect vertex-corrections and effects of self-consistency. The screened interaction is usually evaluated in the random phase approximation, also neglecting vertex- and selfconsistency-corrections. How is it possible that such crude approximations lead to such nice results? The Eindhoven group has spent several years on trying to answer this question. Emphasis was put on the evaluation of next to leading order corrections. The general pattern found is that the corrections are not negligible piece by piece, but that subtle cancellations occur among them. An overview will be given of the obtained results for model and realistic systems.

First-principles calculation of the dynamic image potential for electrons at an Al(111) surface

I.D. White, R.W. Godby(*), M.M. Rieger, R.J. Needs

Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE.

(*) Department of Physics, University of York, Heslington, York YO1 5DD

Analysis of spectroscopic or diffraction experiments involving electrons at surfaces requires a knowledge of the potential experienced by the electrons. According to classical electrostatics an electron near a metal surface moves in an image potential, inversely proportional to distance from the metal-vacuum interface. Density-functional theory (DFT), performed within the local density approximation (LDA) for exchange and correlation, completely fails to reproduce the correct long-range image tail, as this is an inherently non-local effect. The DFT exchange-correlation potential is also only strictly appropriate for describing the potential felt by the ground-state density, as opposed to electrons in excited states such as image states or diffracted electrons in LEED.

Using the new space-time method for many-body perturbation theory calculations [1], we obtain the non-local, energy dependent self-energy Sigma(r,r',E) at an Al(111) surface within the GW approximation. This is the analogue of the exchange-correlation potential in DFT, but naturally includes the correct long-range behaviour by treating exchange and correlation from first principles. The space-time method allows us to obtain information about both energy dependence and quasiparticle state lifetimes without the use of a plasmon-pole approximation. We are then able to examine the effective local potential experienced by excited quasiparticle states as a function of energy, using a localised wavepacket technique which exploits the relatively local character of the self-energy in the vacuum.

1. "Space-time method for ab initio calculation of self-energies and dielectric response functions of solids", H.N. Rojas, R.W. Godby and R.J. Needs, Phys. Rev. Lett. 74 1827 (1995)

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