Efficient implementation of the GW approximation within the all-electron FLAPW method
Abstract
We present an implementation of the GW approximation for the electronic self-energy within the full-potential linearized augmented-plane-wave (FLAPW) method. The algorithm uses an all-electron mixed product basis for the representation of response matrices and related quantities. This basis is derived from the FLAPW basis and is exact for wave-function products. The correlation part of the self-energy is calculated on the imaginary-frequency axis with a subsequent analytic continuation to the real axis. As an alternative we can perform the frequency convolution of the Green function G and the dynamically screened Coulomb interaction W explicitly by a contour integration. The singularity of the bare and screened interaction potentials gives rise to a numerically important self-energy contribution, which we treat analytically to achieve good convergence with respect to the k -point sampling. As numerical realizations of the GW approximation typically suffer from the high computational expense required for the evaluation of the nonlocal and frequency-dependent self-energy, we demonstrate how the algorithm can be made very efficient by exploiting spatial and time-reversal symmetry as well as by applying an optimization of the mixed product basis that retains only the numerically important contributions of the electron-electron interaction. This optimization step reduces the basis size without compromising the accuracy and accelerates the code considerably. Furthermore, we demonstrate that one can employ an extrapolar approximation for high-lying states to reduce the number of empty states that must be taken into account explicitly in the construction of the polarization function and the self-energy. We show convergence tests, CPU timings, and results for prototype semiconductors and insulators as well as ferromagnetic nickel.
- Publication:
-
Physical Review B
- Pub Date:
- March 2010
- DOI:
- 10.1103/PhysRevB.81.125102
- arXiv:
- arXiv:1003.0316
- Bibcode:
- 2010PhRvB..81l5102F
- Keywords:
-
- 71.15.Qe;
- 71.20.Mq;
- 71.45.Gm;
- Excited states: methodology;
- Elemental semiconductors;
- Exchange correlation dielectric and magnetic response functions plasmons;
- Condensed Matter - Materials Science
- E-Print:
- Phys. Rev. B 81, 125102 (2010)