  To obtain accurate independent-particle descriptions for ferromagnetic
two-dimensional van der Waals materials, we apply the quasiparticle
self-consistent $GW$ (QSGW) method to VI$_3$, CrI$_3$, CrGeTe$_3$, and
Fe$_3$GeTe$_2$. QSGW provides a description of the nonlocal
exchange-correlation term in the one-particle Hamiltonian. The nonlocal term is
important not only as the $U$ of density functional theory (DFT)+$U$ but also
for differentiating occupied and unoccupied states in semiconductors. We show
the limitations of DFT+$U$ in mimicking QSGW.
