  We investigate the critical scaling of the spin-1/2 antiferromagnet on the
square lattice in the easy-plane (XXZ) regime, via numerical measurements of
the entanglement entropy constructed from the zeroes of a polynomial ring. We
relate these results to conformal field theory predictions for the area law
scaling of entanglement entropyin the vicinity of quantum critical points in
gapless conformally invariant 2d quantum systems, and in gapless systems with
finite Fermi surfaces. Our measurements are focused in three low-temperature
regions at fixed XXZ anisotropies of $\Delta=1.01$, $\Delta=1.78$ and
$\Delta=2.0$ which probe the quantum regime between the N\'eel point and Ising
phase.
