  We study the higher-order topological spin phases based on a spin analogue of
Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum
Monte Carlo simulations. A continuous N\'eel-valence bond solid quantum phase
transition is revealed by tuning the ratio between dimerized spin couplings,
namely, the weak and strong exchange couplings. Through the finite-size scaling
analysis, we identify the phase critical points, and consequently, map out the
full phase diagrams in related parameter spaces. Particularly, we find that the
valence bond solid phase can be a higher-order topological spin phase, which
has a gap for spin excitations in the bulk while demonstrates characteristic
gapless spin modes at corners of open lattices. We further discuss the
connection between the higher-order topological spin phases and the electronic
correlated higher-order phases, and find both of them possess gapless spin
corner modes that are protected by higher-order topology. Our result
exemplifies higher-order physics in the correlated spin systems and will
contribute to further understandings of the many-body higher-order topological
phenomena.
