Mixed Stochastic-Deterministic Approach for GW Calculations

Many-body perturbation theory in the form of first-principles GW calculations is an established method of obtaining accurate quasiparticle properties of materials. However, traditional approaches based on both the Sternheimer equation and sum-over-bands approaches scale quarticly in system size and can be notoriously difficult to converge. Fully stochastic methods which scale linearly can handle very large systems, but often use real-time and real-space propagation that requires custom codes and efficient evaluation of the Kohn-Sham Hamiltonian's action on a trial vector. Here we present a combined stochastic-deterministic approach to reciprocal-space GW calculations that achieves quasi-quadratic scaling while incurring negligible error, <100 meV in quasiparticle energies. Our method displays smooth convergence, and we benchmark on a variety of systems spanning dimensionality, screening, and size. Implementation is straightforward in existing reciprocal-space GW codes and allows the calculation and convergence of large systems without a fully stochastic, real-time formalism.