Efficient dielectric matrix calculations using the Lanczos algorithm for fast many-body $G_0{W}_0$ implementations

Abstract

We present a $G_0{W}_0$ implementation that assesses the two major bottlenecks of traditional plane-waves implementations, the summations over conduction states and the inversion of the dielectric matrix, without introducing new approximations in the formalism. The first bottleneck is circumvented by converting the summations into Sternheimer equations. Then, the novel avenue of expressing the dielectric matrix in a Lanczos basis is developed, which reduces the matrix size by orders of magnitude while being computationally efficient. We also develop a model dielectric operator that allows us to further reduce the size of the dielectric matrix without accuracy loss. Furthermore, we develop a scheme that reduces the numerical cost of the contour deformation technique to the level of the lightest plasmon pole model. Finally, the use of the simplified quasi-minimal residual scheme in replacement of the conjugate gradients algorithm allows a direct evaluation of the $G_0{W}_0$ corrections at the desired real frequencies, without need for analytical continuation. The performance of the resulting $G_0{W}_0$ implementation is demonstrated by comparison with a traditional plane-waves implementation, which reveals a 500-fold speedup for the silane molecule. Finally, the accuracy of our $G_0{W}_0$ implementation is demonstrated by comparison with other $G_0{W}_0$ calculations and experimental results.

19 pages, 2 figures

References in corpus (7)

• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Turbo charging time-dependent density-functional theory with Lanczos chains
• Efficient solution of Poisson's equation with free boundary conditions
• Optical excitations in organic molecules, clusters and defects studied by first-principles Green's function methods
• Band convergence and linearization error correction of all-electron GW calculations: The extreme case of zinc oxide
• Band Offsets at the Si/SiO${}_2$ Interface from Many-Body Perturbation Theory
• Quantitative Molecular Orbital Energies within a $G_0{W}_0$ Approximation