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We study the quantum phase diagram of a system of hard-core bosons on theKagome lattice with nearest-neighbor repulsive interactions, for arbitrarydensities, by means of the hierarchical mean field theory and exactdiagonalization techniques. This system is isomorphic to the spin S=1/2 XXZmodel in presence of an external magnetic field, a paradigmatic example offrustrated quantum magnetism. In the non-frustrated regime, we find two crystalphases at densities 1/3 and 2/3 that melt into a superfluid phase whenincreasing the hopping amplitude, in semi-quantitative agreement with quantumMonte Carlo computations. In the frustrated regime and away from half-filling,we find a series of plateaux with densities commensurate with powers of 1/3.The broader density plateaux (at densities 1/3 and 2/3) are remnants of theclassical degeneracy in the Ising limit. For densities near half-filling, thisstaircase of crystal phases melts into a superfluid, which displays finitechiral currents when computed with clusters having an odd number of sites. Boththe staircase of crystal phases and the superfluid phase prevail in thenon-interacting limit, suggesting that the lowest dispersionlesssingle-particle band may be at the root of this phenomenon.

Staircase of crystal phases of hard-core bosons on the Kagome lattice