Low rank approximation in G 0 W 0 calculations
Abstract
The single particle energies obtained in a KohnSham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photoemission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a manybody perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a noninteracting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cost of $G_0W_0$ calculation can be reduced by constructing a low rank approximation to the frequency dependent part of $W_0$. In particular, we examine the effect of such a low rank approximation on the accuracy of the $G_0W_0$ approximation. We also discuss how the numerical convolution of $G_0$ and $W_0$ can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.
 Publication:

Science in China A: Mathematics
 Pub Date:
 August 2016
 DOI:
 10.1007/s114250160296x
 arXiv:
 arXiv:1605.02141
 Bibcode:
 2016ScChA..59.1593S
 Keywords:

 Mathematics  Numerical Analysis;
 Physics  Computational Physics
 EPrint:
 The paper has been accepted for publication in SCIENCE CHINA Mathematics