Superfluid-insulator transitions of bosons on the kagome lattice at noninteger fillings

We study the superfluid-insulator transitions of bosons on the kagome lattice at incommensurate filling factors f=1/2 and 2/3 using a duality analysis. We find that at f=1/2 the bosons will always be in a superfluid phase and demonstrate that the T-3 symmetry of the dual (dice) lattice, which results in dynamic localization of vortices due to the Aharonov-Bohm caging effect, is at the heart of this phenomenon. In contrast, for f=2/3, we find that the bosons exhibit a quantum phase transition between superfluid and translational symmetry broken Mott insulating phases. We discuss the possible broken symmetries of the Mott phase and elaborate the theory of such a transition. Finally we map the boson system to a XXZ spin model in a magnetic field and discuss the properties of this spin model using the obtained results.