# Complex time, shredded propagator method for large-scale GW calculations

## TL;DR

This paper introduces a novel cubic-scaling GW computational method using complex time propagators and energy partitioning, enabling more efficient large-scale electronic structure calculations.

## Contribution

The paper presents a new GW approach that recasts equations as Fourier-Laplace integrals and employs shredding and quadrature, significantly reducing computational scaling.

## Key findings

- Outperforms standard quartic methods on small systems
- Achieves substantial speedup over other cubic methods
- Applicable to large and complex assemblies

## Abstract

The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to large complex assemblies due to its large computational overhead and quartic scaling with particle number. Here, the GW equations are recast, exactly, as Fourier-Laplace time integrals over complex time propagators. The propagators are then "shredded" via energy partitioning and the time integrals approximated in a controlled manner using generalized Gaussian quadrature(s) while discrete variable methods are employed to represent the required propagators in real-space. The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems ($\gtrapprox$ 10 atoms) and also represents a substantial improvement over other cubic methods tested for all system sizes studied. The approach can be applied to any theoretical framework containing large sums of terms with energy differences in the denominator.