  A universal finite system-size scaling analysis of the entanglement entropy
is presented for highly degenerate ground states arising from spontaneous
symmetry breaking with type-B Goldstone modes in exactly solvable
one-dimensional quantum many-body systems. These states appear to be
scale-invariant, but not conformally invariant. Our findings are based on a
physical argument, imposing three constraints on the entanglement entropy, in
addition to further confirmation from an asymptotic analysis of the
entanglement entropy for the ${\rm SU}(2)$ spin-$1/2$ ferromagnetic states. The
resulting universal scaling form is demonstrated for three fundamental models
-- the ${\rm SU}(2)$ spin-$s$ Heisenberg ferromagnetic model, the ${\rm
SU}(N+1)$ ferromagnetic model, and the staggered ${\rm SU}(3)$ spin-1
ferromagnetic biquadratic model. The results point towards a classification for
distinct types of scale-invariant states, relevant to a complete classification
of quantum states of matter.
