  We analyze the critical properties and the entanglement scaling at the
quantum critical points of the spin-half XY model on the two-dimensional
square-lattice bilayer and necklace lattice, based on quantum Monte Carlo
simulations on finite tori and for different subregion shapes. For both models,
the finite-size scaling of the transverse staggered spin structure factor is
found in accord with a quantum critical point described by the two-component,
three-dimensional $\phi^4$-theory. The second R\'enyi entanglement entropy in
the absence of corners along the subsystem boundary exhibits area-law scaling
in both models, with an area-law prefactor of $0.0674(7)$ [$0.0664(4)$] for the
bilayer [necklace] model, respectively. Furthermore, the presence of
$90^{\circ}$ corners leads to an additive logarithmic term in both models. We
estimate a contribution of $-0.010(2)$ [$-0.009(2)$] due to each $90^{\circ}$
corner to the logarithmic correction for the bilayer [necklace] model, and
compare our findings to recent numerical linked cluster calculations and series
expansion results on related models.

Strongly Correlated Electrons