  Different from the spin-1 Haldane gapped phase, we propose a novel SO(3)
spin-1 matrix product state (MPS), whose parent Hamiltonian includes three-site
spin interactions. From the entanglement spectrum of a single block with $l$
sites, an enlarged SU(3) symmetry is identified in the edge states, which are
conjugate to each other for the $l=even$ block but identical for the $l=odd$
block. By blocking this novel state, the blocked MPS explicitly displays the
SU(3) symmetry with two distinct structures. Under a symmetric bulk bipartition
with a sufficient large block length $% l=even$, the entanglement Hamiltonian
(EH) of the reduced system characterizes a spontaneous dimerized phase with
two-fold degeneracy. However, for the block length $l=odd$, the corresponding
EH represents an SU(3) quantum critical point with delocalized edge
quasiparticles, and the critical field theory is described by the SU(3) level-1
Wess-Zumino-Witten conformal field theory.
