Spinor bosons realization of the SU(3) Haldane phase with adjoint representation

The Haldane phase with local SU(3) adjoint representation constitutes the simplest non-trivial symmetry-protected topological phases in the SU($N>2$) Heisenberg spin chains. In this paper, we propose to realize this phase by a two-species spinor Bose gas, with each species labeling the quark or antiquark states of SU(3) symmetry. In the strong-coupling limit, we determine the ground-state phase diagram, and identify a quantum phase transition from the Haldane phase to a dimer phase. We show how to characterize the Haldane phase through its edge excitations. We also explain the physics at the dimer phase, by constructing an explicit ground-state ansatz at the dimer point.