Correlations and entanglement in quantum critical bilayer and necklace XY models

Abstract

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.