  A generic scheme is proposed to perform a finite-entanglement scaling
analysis for scale-invariant states, which appear to be highly degenerate
ground states arising from spontaneous symmetry breaking with type-B Goldstone
modes. This allows us to extract the number of type-B Goldstone modes and the
dynamical critical exponent, in combination with a finite block-size scaling
analysis, from numerical simulations of quantum many-body systems in the
context of tensor network representations. The number of type-B Goldstone modes
is identical to the fractal dimension, thus reflecting an abstract fractal
underlying the ground state subspace. As illustrative examples, we investigate
the spin-$s$ Heisenberg ferromagnetic model, the $\rm{SU}(3)$ ferromagnetic
model and the $\rm{SO}(4)$ spin-orbital model.
