Full-frequency GW without frequency

Area of Science:

• Computational Quantum Chemistry
• Many-Body Perturbation Theory

Background:

• Efficient computation of the GW approximation is crucial for materials science and chemistry.
• Frequency integrals in GW calculations are numerically challenging, often requiring approximations or leading to high computational costs.

Purpose of the Study:

• Introduce a novel formulation of the full-frequency GW approximation.
• Reduce the computational scaling of GW calculations.
• Provide new theoretical insights into the GW approximation and its relation to other quantum chemical methods.

Main Methods:

• Recasting the GW approximation as an eigenvalue problem in an expanded space.
• Utilizing iterative eigensolvers and a density-fitted implementation.
• Avoiding time/frequency grids and the common 'diagonal' approximation.

Main Results:

• Achieved a reduction in computational scaling from O(N^6) to O(N^5) with iterative eigensolvers, and to O(N^4) with a density-fitted approach.
• Demonstrated numerical verification of the predicted scaling behaviors.
• Found the new formulation competitive with existing O(N^4) methods.

Conclusions:

• The new eigenvalue formulation offers a more efficient and theoretically insightful approach to GW calculations.
• This formulation clarifies the connections between GW, configuration interaction, coupled-cluster theory, and algebraic diagrammatic construction.
• Opens new avenues for improving the GW approximation.