  We study the quantum critical phase of a SU(2) symmetric spin-2 chain
obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling
of the entanglement entropy and finite-size energies by exact diagonalization
and density-matrix renormalization group methods. From the numerical results of
the energy spectrum, central charge, and scaling dimension we identify the
conformal field theory describing the whole critical phase to be the SU(3)$_1$
Wess-Zumino-Witten model. We find that while in the whole critical phase the
Hamiltonian is only SU(2) invariant, there is an emergent SU(3) symmetry in the
thermodynamic limit.
