Elimination of unoccupied state summations in ab-initio self-energy calculations for large supercells

TL;DR

This paper introduces a novel iterative method for calculating self-energy corrections in large supercells that removes the need for summing over unoccupied states, significantly enhancing computational efficiency.

Contribution

It develops an iterative Green's function expansion approach that reduces the scaling of self-energy calculations from fourth to third power of the system size.

Findings

Reduces computational scaling from O(N^4) to O(N^3)

Improves efficiency for systems with 8 or more silicon atoms

Eliminates explicit unoccupied state summations

Abstract

We present a new method for the computation of self-energy corrections in large supercells. It eliminates the explicit summation over unoccupied states, and uses an iterative scheme based on an expansion of the Green's function around a set of reference energies. This improves the scaling of the computational time from the fourth to the third power of the number of atoms for both the inverse dielectric matrix and the self-energy, yielding improved efficiency for 8 or more silicon atoms per unit cell.