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To obtain accurate independent-particle descriptions for ferromagnetictwo-dimensional van der Waals materials, we apply the quasiparticleself-consistent $GW$ (QSGW) method to VI$_3$, CrI$_3$, CrGeTe$_3$, andFe$_3$GeTe$_2$. QSGW provides a description of the nonlocalexchange-correlation term in the one-particle Hamiltonian. The nonlocal term isimportant not only as the $U$ of density functional theory (DFT)+$U$ but alsofor differentiating occupied and unoccupied states in semiconductors. We showthe limitations of DFT+$U$ in mimicking QSGW.

Role of non-locality in exchange-correlation for magnetic 2D van der Waals materials