SU(3) quantum critical model emerging from a spin-1 topological phase

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 $$, 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.