We obtain the complete phase diagram of the hardcore Bose-Hubbard model inthe presence of a period-two superlattice in two and three dimensions. First weacquire the phase boundaries between the superfluid phase and the `trivial'insulating phases of the model (the completely-empty and completely-filledlattices) analytically. Next, the boundary between the superfluid phase and thehalf-filled Mott-insulating phase is obtained numerically, using the stochasticseries expansion (SSE) algorithm followed by finite-size scaling. We alsocompare our numerical results against the predictions of several approximationschemes, including two mean-field approaches and a fourth-order strong-couplingexpansion (SCE), where we show that the latter method in particular issuccessful in producing an accurate picture of the phase diagram. Finally, weexamine the extent to which several approximation schemes, such as the randomphase approximation and the strong-coupling expansion, give an accuratedescription of the momentum distribution of the bosons inside the insulatingphases.
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