We study a one-dimensional model of interacting bosons on a lattice with two flat bands. Regular condensation is suppressed due to the absence of a well-defined minimum in the single-particle spectrum. We find that interactions stabilize a number of nontrivial phases such as a pair (quasi)condensate, a supersolid at incommensurable fillings, and valence bond crystals at commensurability. We support our analytical calculations with numerical simulations using the density matrix renormalization group technique. Implications for cold atoms are discussed.
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Tovmasyan et al. (2013) studied this question.
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