Improving stochastic Green’s function methods for localized states in low-dimensional heterostructures

First, we present a new embedding approach [1] in the stochastic GW technique that enables efficient treatment of the impurity states with high accuracy and minimal effort. The method is based on a partitioning of the Green’s function and screened Coulomb potential into the deterministic subspace (of localized states) and the stochastic subspace. The enhanced stochastic-deterministic sampling minimizes statistical errors in energies of localized quasiparticles.
Further, we present a new technique for the stochastic decomposition of the many-body interactions into additive subspace contributions. We partition the Hilbert space and compute the polarization self-energy via sampling selected charge density fluctuations in real space and time. The method allows to identify couplings among different areas, e.g., screening contributions in quantum interfaces.
We exemplify our approaches on N-vacancy defects in monolayer and hBN - graphene bilayer (> 2,000 electrons). We demonstrate the new hybrid approach reduces statistical errors and leads to significant savings in computational time.
1. M. Romanova, V. Vlcek, J. Chem. Phys. 153, 134103, 2020