Spin-dependent Stochastic GW Calculations and Vertex correction

We extend the stochastic GW (sGW) formalism to fully spin-polarized systems, encompassing both collinear and non-collinear spin configurations. For non-collinear systems—where Kohn–Sham states are complex two-component spinors—we construct a complex stochastic basis that preserves the real-valued stochastic charge at time zero, enabling unbiased evaluation of the random-phase approximation (RPA) screened interaction for spinors. Through systematic error analysis and validation on representative materials, we demonstrate that the computational scaling of collinear sGW remains identical to the spin-unpolarized case, while the non-collinear sGW exhibits only a modest two-to-three-fold overhead and retains linear scaling. This unified treatment of spin within a single scalable stochastic framework opens the door to routine many-body predictions for large magnetic and spin–orbit-coupled systems.

Building on this foundation, we are incorporating nonlocal spin-vertex corrections into the sGW framework to capture beyond-RPA exchange–correlation effects and spin-dependent screening. These extensions will provide a more accurate description of spin fluctuations and collective excitations, further enhancing the predictive power of sGW for strongly correlated and topologically nontrivial magnetic materials.