Symmetry-protected Topological Phases in Spinful Bosons with a Flat Band

We theoretically demonstrate that interacting symmetry-protected topological (SPT) phases can be realized with ultracold spinful bosonic atoms loaded on lattices which has a flat band at the bottom of the band structure. Ground states of such systems are not conventional Mott insulators. We find that the many-body ground states can be exactly written down when certain parameters in the Hamiltonians are properly chosen. The spin and charge fluctuations at zero temperature together determine the SPT phases of the system, and the exact ground state turns out to serve as a representative state of the SPT phases. We study some concrete examples. In particular, we demonstrate that spin-1 bosons on a sawtooth chain can be in an SPT phase protected by Z₂×Z₂ spin rotation symmetry or time-reversal symmetry, and this SPT phase is a result of the spin fluctuation. We also show that spin-3 bosons on a kagome lattice can be in an SPT phase protected by D₂ point group symmetry, this SPT phase is however a result of the charge fluctuation.