Efficient implementation of the GW approximation within the all-electron FLAPW method

C. Friedrich, S. Blügel, A. Schindlmayr, Physical Review B 81 (2010).

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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.
Publishing Year
Journal Title
Physical Review B
Volume
81
Issue
12
Article Number
125102
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Friedrich C, Blügel S, Schindlmayr A. Efficient implementation of the GW approximation within the all-electron FLAPW method. Physical Review B. 2010;81(12). doi:10.1103/PhysRevB.81.125102
Friedrich, C., Blügel, S., & Schindlmayr, A. (2010). Efficient implementation of the GW approximation within the all-electron FLAPW method. Physical Review B, 81(12). https://doi.org/10.1103/PhysRevB.81.125102
@article{Friedrich_Blügel_Schindlmayr_2010, title={Efficient implementation of the GW approximation within the all-electron FLAPW method}, volume={81}, DOI={10.1103/PhysRevB.81.125102}, number={12125102}, journal={Physical Review B}, publisher={American Physical Society}, author={Friedrich, Christoph and Blügel, Stefan and Schindlmayr, Arno}, year={2010} }
Friedrich, Christoph, Stefan Blügel, and Arno Schindlmayr. “Efficient Implementation of the GW Approximation within the All-Electron FLAPW Method.” Physical Review B 81, no. 12 (2010). https://doi.org/10.1103/PhysRevB.81.125102.
C. Friedrich, S. Blügel, and A. Schindlmayr, “Efficient implementation of the GW approximation within the all-electron FLAPW method,” Physical Review B, vol. 81, no. 12, 2010.
Friedrich, Christoph, et al. “Efficient Implementation of the GW Approximation within the All-Electron FLAPW Method.” Physical Review B, vol. 81, no. 12, 125102, American Physical Society, 2010, doi:10.1103/PhysRevB.81.125102.
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