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We investigate the critical scaling of the spin-1/2 antiferromagnet on thesquare lattice in the easy-plane (XXZ) regime, via numerical measurements ofthe entanglement entropy constructed from the zeroes of a polynomial ring. Werelate these results to conformal field theory predictions for the area lawscaling of entanglement entropyin the vicinity of quantum critical points ingapless conformally invariant 2d quantum systems, and in gapless systems withfinite Fermi surfaces. Our measurements are focused in three low-temperatureregions 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 Isingphase.

Nonperturbative Renormalization of the Heisenberg Spin-1/2 Antiferromagnet on the Square Lattice