Correlations and entanglement in quantum critical bilayer and necklace XY models

We analyze the critical properties and the entanglement scaling at the quantum critical points of the spin-half XY model on a 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 empty set(4) theory. The second Renyi 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 degrees 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 degrees 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.