  It is argued that highly degenerate ground states arising from spontaneous
symmetry breaking with a type-B Goldstone mode are scale-invariant, with a
salient feature that the entanglement entropy $S(n)$ scales logarithmically
with the block size $n$ in the thermodynamic limit. As it turns out, the
prefactor is half the number of type-B Goldstone modes $N_B$. This is achieved
by performing an exact singular value decomposition of the degenerate ground
states, thus unveiling their self-similarities - the essence of a fractal.
Combining with a field-theoretic prediction [O. A. Castro-Alvaredo and B.
Doyon, Phys. Rev. Lett. \textbf{108}, 120401 (2012)], we are led to the
identification of the fractal dimension $d_f$ with the number of type-B
Goldstone modes $N_B$ for quantum many-body systems undergoing spontaneous
symmetry breaking.
