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We investigate the behaviour of hard-core bosons in one- and two-dimensionalflat band systems, the chequerboard and the kagom\'e lattice andone-dimensional analogues thereof. The one dimensional systems have an exactlocal reflection symmetry which allows for exact results. We show that abovethe critical density an additional particle forms a pair with one of the otherbosons and that the pair is localised. In the two-dimensional systems exactresults are not available but variational results indicate a similar physicalbehaviour.

Hard-core bosons in flat band systems above the critical density