  We explore the R\'enyi entanglement entropies of a one-dimensional (line)
subsystem of length $L$ embedded in two-dimensional $L\times L$ square lattice
for quantum spin models whose ground-state breaks a continuous symmetry in the
thermodynamic limit. Using quantum Monte Carlo simulations, we first study the
$J_1 - J_2$ Heisenberg model with antiferromagnetic nearest-neighbor $J_1>0$
and ferromagnetic second-neighbor couplings $J_2\le 0$. The signature of SU(2)
symmetry breaking on finite size systems, ranging from $L=4$ up to $L=40$
clearly appears as a universal additive logarithmic correction to the R\'enyi
entanglement entropies: $l_q \ln L$ with $l_q\simeq 1$, independent of the
R\'enyi index and values of $J_2$. We confirm this result using a high
precision spin-wave analysis (with restored spin rotational symmetry) on finite
lattices up to $10^5\times 10^5$ sites, allowing to explore further
non-universal finite size corrections and study in addition the case of U(1)
symmetry breaking. Our results fully agree with the prediction $l_q=n_G/2$
where $n_G$ is the number of Goldstone modes, by Metlitski and Grover
[arXiv:1112.5166].
