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

Extracting the number of type-B Goldstone modes and the dynamical critical exponent for a type of scale-invariant states