  Electronic correlations could have significant impact on the material
properties. They are typically pronounced for localized orbitals and enhanced
in low-dimensional systems, so two-dimensional (2D) transition metal compounds
could be a good platform to study their effects. Recently, a new class of 2D
transition metal compounds, the MoSi$_2$N$_4$-family materials, have been
discovered, and some of them exhibit intrinsic magnetism. Here, taking
monolayer VSi$_{2}$P$_{4}$ as an example from the family, we investigate the
impact of correlation effects on its physical properties, based on the
first-principles calculations. We find that different correlation strength can
drive the system into a variety of interesting ground states, with rich
magnetic, topological and valley features. With increasing correlation
strength, while the system favors a ferromagnetic semiconductor state for most
cases, the magnetic anisotropy and the band gap type undergo multiple
transitions, and in the process, the band edges can form single, two or three
valleys for electrons or holes. Remarkably, there is a quantum anomalous Hall
(QAH) insulator phase, which has a unit Chern number. The boundary of the QAH
phase correspond to the half-valley semimetal state with fully valley polarized
bulk carriers. We further show that for phases with the out-of-plane magnetic
anisotropy, the interplay between spin-orbit coupling and orbital character of
valleys enable an intrinsic valley polarization for electrons but not for
holes. This electron valley polarization can be switched by reversing the
magnetization direction, providing a new route of magnetic control of
valleytronics. Our result sheds light on the possible role of correlation
effects in the 2D transition metal compounds, and it will open new perspectives
for spintronic, valleytronic and topological nanoelectronic applications based
on these materials.
