We give a bosonic realization of the SU(3) antiferromagnetic Heisenberg (AFH) chain in the alternating conjugate representation, and study its phase diagram as a function of staggered interactions and anisotropy along the $T^3$ and $T^8$ directions. Unlike the SU(2) case, we observe a chiral-reversed quantum phase transition, where each competing phase is adiabatically connected to one of the chiral Haldane phases predicted in the SU(3) AFH chain with local adjoint representation. In the vicinity of the Heisenberg point, we identify a symmetry-protected topological state that appears at the first excited energy level. We also study the spontaneous ${\mathbb{Z}}_3$ symmetry breaking of the system, and provide a variational wave function that captures the transition from the topological phase to the trivial phase. Finally, we propose an experimental realization of our bosonic model by two spin-1/2 bosons in an optical lattice.

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• Spontaneous symmetry breaking
• Symmetry protected topological states
• Topological phase transition
• Spinor Bose-Einstein condensates
• Heisenberg model
• SU(N) symmetries