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

TL;DR

This paper introduces an efficient all-electron implementation of the GW approximation within the FLAPW method, optimizing response matrix representation and exploiting symmetries for computational efficiency, with applications to semiconductors, insulators, and nickel.

Contribution

The paper presents a novel, efficient GW implementation in the FLAPW method using a mixed product basis and symmetry exploitation, reducing computational costs.

Findings

Achieved good convergence with respect to k-point sampling.

Demonstrated computational efficiency through symmetry and basis optimization.

Validated the method on semiconductors, insulators, and ferromagnetic nickel.

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 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. 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.