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

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.