  The field of two-dimensional (2D) materials has grown dramatically in the
last two decades. 2D materials can be utilized for a variety of next-generation
optoelectronic, spintronic, clean energy, and quantum computation applications.
These 2D structures, which are often exfoliated from layered van der Waals
(vdW) materials, possess highly inhomogeneous electron densities and can
possess short- and long-range electron correlations. The complexities of 2D
materials make them challenging to study with standard mean-field electronic
structure methods such as density functional theory (DFT), which relies on
approximations for the unknown exchange-correlation functional. In order to
overcome the limitations of DFT, highly accurate many-body electronic structure
approaches such as Diffusion Monte Carlo (DMC) can be utilized. In the past
decade, DMC has been used to calculate accurate magnetic, electronic,
excitonic, and topological properties in addition to accurately capturing
interlayer interactions and cohesion and adsorption energetics of 2D materials.
This approach has been applied to 2D systems of wide interest including
graphene, phosphorene, MoS$_2$, CrI$_3$, VSe$_2$, GaSe, GeSe, borophene, and
several others. In this review article, we highlight some successful recent
applications of DMC to 2D systems for improved property predictions beyond
standard DFT.
