Abstract
Ultracold bosons in optical superlattices are expected to exhibit fractional-filling insulating phases for sufficiently large repulsive interactions. On strictly one-dimensional systems, the exact mapping between hard-core bosons and free spinless fermions shows that any periodic modulation in the lattice parameters causes the presence of fractional-filling insulator domains. Here, we focus on two recently proposed realistic two-dimensional structures where such mapping does not hold, i.e., the two-leg ladder and the trimerized kagom\'e lattice. Based on a cell strong-coupling perturbation technique, we provide quantitatively satisfactory phase diagrams for these structures, and give estimates for the occurrence of the fractional-filling insulator domains in terms of the intercell to intracell hopping amplitude ratio.
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