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In this paper, we derive corrections to the subleading logarithmic term ofthe entanglement entropy in systems with spontaneous broken continuoussymmetry. Using quantum Monte Carlo simulations, we show that the improvedscaling formula leads to much better estimations of the number of Goldstonemodes in the two-dimensional square lattice spin-1/2 Heisenberg model andbilayer spin-1/2 Heisenberg model in systems of rather small sizes, comparedwith previous results. In addition, the universal geometry-dependent finiteconstant in the entanglement entropy scaling is also obtained in good agreementwith the theoretical value.

Improved scaling of the entanglement entropy of quantum antiferromagnetic Heisenberg systems