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The topological properties of hardcore bosons on ribbons of honeycomb latticeare studied using quantum Monte Carlo simulations. We map out a rich phasediagram with the superfluid and insulator phases at various fillings.Particularly, it is revealed that the insulator state at half filling is atopological bosonic state, which is characterized by a nontrivial Berry phaseand a pair of edge states. We provide intuitive picture to understand thistopological bosonic insulator state by showing that it can be adiabaticallymapped to a topological fermionic model. It is also shown that the topologicaledge states are robust against weak interactions beyond the hardcore repulsion.Our results can be simulated by using bosonic cold atoms trapped in designedoptical lattices.

Topological bosonic states on ribbons of honeycomb lattice