Computational Many Body Perturbation Theory
The principal direction of this work, based mainly in the York and Cambridge groups, has been the ab initio application of many-body perturbation theory to real condensed-matter systems. Recent projects include the determination of the effective potential for electrons at an A1(111) surface, including dynamic image effects [7], and the first GW determination of the charge densities of materials [8]. We have also developed a new suite of programs, based on the representation of all non-local many-body quantities in real space and imaginary time, rather than the momentum energy representation familiar in solid state physics. This "space-time" method [10, 11, and PRL in 1995] offers great computational advantages, arising primarily from the fact that the two most time consuming steps in the calculation change from seven-dimensional convolutions to simple multiplications when written in the space-time representation (see below). Collaborative work based on our programs but based elsewhere includes the elimination of the sum over unoccupied states that appears in conventional perturbation theory for the self-energy [2] . A fruitful strand of the research has been the use of Hubbard-model systems (for which the many-body problem may be solved exactly) to assess the performance of the GW approximation itself (including variants of it), and candidate extensions to it that may be of use for stronger electronic correlation [e.g. 5, 9].
We have recently started a major investigation of the applications of expressions from many body perturbation theory for the total energy of many-electron systems to ab initio calculations for real matter. The aim is to overcome the limitations of the usual density-based functionals within density-functional theory (such as the LDA and GGAs). In the initial phase of the project, we have performed very precise calculations of the self-consistent GW total energy of the homogeneous three- and two-dimensional electron gases over a wide range of densities [13]. The results are very promising: for instance, in the 3D gas, the the energy is within 2 mHa/electron of the exact results over a wide range of densities. Applications to inhomogeneous systems are in progress. In parallel with this work, we have also developed a highly simplified and efficient version of the total energy method, formulated within the framework of generalised Kohn-Sham density-functional theory, in which the usual local exchange-correlation potential is replaced by a non-local potential. Initial results [12] are promising and indicate the fundamentally physical nature of the non-locality of the potential.
A further theme in our work has been the uncovering of pathological aspects of the total-energy functional (of the electron density) that underlies Kohn-Sham density-functional theory [1,3,4]. CCP9 funding has been helpful in allowing some travel between the York and Cambridge groups, particularly for papers [5,6,7,8,9,10,11] below.
Key recent papers
- "Density-functional theory of polar insulators",
X. Gonze, Ph. Ghosez and R.W. Godby,
Phys. Rev. Lett. 78 294 (1997). - "Elimination of unoccupied state summations in ab initio self-energy
calculations for large supercells",
L. Reining, G. Onida and R.W. Godby,
Phys. Rev. B (Rapid Communications) 56 R4301 (1997). - "Polarization-Dependence of the Exchange Energy",
X. Gonze, Ph. Ghosez and R.W. Godby,
Phys. Rev. Lett. 78 2029 (1997). - "The long-wavelength behaviour of the exchange-correlation kernel
in the Kohn-Sham theory of
periodic systems",
Ph. Ghosez, X. Gonze and R. W. Godby,
Phys. Rev. B 56 12811-12817 (1997). - "Systematic vertex corrections through iterative solution of Hedin's
equations beyond the GW approximation",
A. Schindimayr and R.W. Godby,
Phys. Rev. Lett. 80 1702 (1998). - "Density-relaxation part of the self energy",
R.W. Godby and LD. White,
Phys. Rev. Lett. 80 3161 (1998). - "Dynamic image potential at an Al (111) surface",
I. D. White, R. W. Godby, M. M. Rieger and R.J. Needs,
Phys. Rev. Lett. 80 4265-8 (1998). - "The charge density of semiconductors in the GW approximation",
Martin M. Rieger and R.W. Godby,
Phys. Rev. B 58 1343-8 (1998). - "Spectra and total energies from self-consistent many-body perturbation
theory",
Arno Schindlmayr, Thomas J. Pollehn and R.W. Godby,
Phys. Rev. B 58 12684-90 (1998). - "The GW space-time method for the self-energy of large systems",
Martin M. Rieger, L. Steinbeck, I. D. White, H. N. Rojas and R. W. Godby,
Computer Physics Communications 117 211-228 (1999). - "Enhancements to the GW space-time method",
L. Steinbeck, A. Rubio, L. Reining, M. Torrent, I.D. White and R.W. Godby,
Computer Physics Communications 125 105-118 (2000). - "Efficient total energy calculations from self-energy models",
Paula S?nchez-Friera and R.W. Godby,
Phys. Rev. Lett. 85 5611-5614 (2000). - "Self-consistent calculation of total energies of the electron gas
using many-body perturbation theory",
P. Garcia-Gonzalez and R.W. Godby,
Phys. Rev. B 63 075112 (2001) (4 pages). - "GW self-energy calculations for surfaces and interfaces",
P. Garcia-Gonzalez and R.W. Godby,
accepted for publication in Computer Physics Communications. - "Diagrammatic self-energy approximations and the total particle number",
Arno Schindlmayr, P. Garcia-Gonzalez and R.W. Godby,
submitted.
Plans for future research
Ongoing and proposed research projects include
- Ab initio total energy calculations from self-consistent many-body perturbation theory (both in full and in a simplified form as a replacement for standard DFT methods)
- Electronic structure of quantum dots, quantum wires and other nanostructures
- Dynamics of electronically molecules on surfaces
Workshops Organised
The European NANOPHASE network (Nanoscale photon absorption and spectroscopy with electrons), funded by the EU as a Research Training Network, is coordinated from the York group. The network has held an annual workshop for several years, most recently in Valladolid (1998) and at CECAM (1997, 1999 and 2000), in the last two cases with additional funding from ESF through Ψk.
