Stochastic Formalism for Fast Spin-Resolved GW

Area of Science:

• Condensed Matter Physics
• Computational Materials Science
• Quantum Chemistry

Background:

• The stochastic GW (sGW) formalism is a powerful tool for electronic structure calculations.
• Previous sGW methods were limited to spin-unpolarized systems.
• Accurate modeling of magnetic materials requires handling spin-polarized electronic states.

Purpose of the Study:

• To extend the sGW formalism to fully spin-polarized systems, including both collinear and noncollinear spin configurations.
• To develop a computational framework for accurate many-body predictions in magnetic materials.

Main Methods:

• Development of a complex-valued stochastic basis for noncollinear spin systems.
• Unbiased evaluation of the random-phase approximation (RPA) screened interaction for spinors.
• Error analysis and testing on real material systems.

Main Results:

• The collinear sGW method maintains the same time complexity as spin-unpolarized sGW.
• Noncollinear sGW is computationally 2-3 times more expensive than spin-unpolarized sGW but scales linearly with low multiplicity.
• A unified, scalable framework for both collinear and noncollinear spin-polarized systems is established.

Conclusions:

• The extended sGW formalism enables routine many-body predictions for large-scale magnetic and spin-orbit-coupled materials.
• This work significantly advances the capability of computational materials science for spintronic applications.