Low-Scaling Algorithms for GW and Constrained Random Phase Approximation Using Symmetry-Adapted Interpolative...

Area of Science:

• Computational Materials Science
• Quantum Chemistry
• Condensed Matter Physics

Background:

• Accurate electronic structure calculations are crucial for understanding material properties.
• Traditional many-body methods often suffer from high computational costs, limiting their application to large systems.
• Incorporating crystal symmetries can significantly improve computational efficiency.

Purpose of the Study:

• To develop low-scaling algorithms for GW and constrained random phase approximation (cRPA) calculations.
• To leverage space-group symmetries for enhanced computational performance in crystalline systems.
• To demonstrate the applicability of these methods for large-scale many-body calculations beyond density functional theory.

Main Methods:

• Symmetry-adapted interpolative separable density fitting (ISDF) procedure.
• Incorporation of space-group symmetries into GW and cRPA formulations.
• Development of algorithms with cubic scaling in system size and linear scaling in k-points.

Main Results:

• Achieved cubic scaling with system size and linear scaling with k-points for GW and cRPA.
• Validated the methods through comparisons with existing literature data.
• Demonstrated efficiency on large-scale systems, including downfolded Hamiltonians for defects in hexagonal boron nitride.

Conclusions:

• The developed ISDF-based methods provide a significant efficiency improvement for many-body calculations.
• These algorithms are generally applicable to crystalline systems, irrespective of the basis set or quasiparticle approximation.
• Highlights the potential of ISDF for tackling large-scale quantum mechanical simulations in materials science.