  Within the framework of many-body perturbation theory (MBPT) integrated with
density functional theory (DFT), a novel defect-subspace projection GW method,
the so-called p-GW, is proposed. By avoiding the periodic defect interference
through open boundary self-energies, we show that the p-GW can efficiently and
accurately describe quasi-particle correlated defect levels in two-dimensional
(2D) monolayer MoS$_2$. By comparing two different defect states originating
from sulfur vacancy and adatom to existing theoretical and experimental works,
we show that our GW correction to the DFT defect levels is precisely modelled.
Based on these findings, we expect that our method can provide genuine trap
states for various 2D transition-metal dichalcogenide (TMD) monolayers, thus
enabling the study of defect-induced effects on the device characteristics of
these materials via realistic simulations.
