Interacting bosons in two-dimensional flat band systems

The Hubbard model of bosons on two dimensional lattices with a lowest flat band is discussed. In these systems there is a critical density, where the ground state is known exactly and can be represented as a charge density wave. Above this critical filling, depending on the lattice structure and the interaction strength, the additional particles are either delocalised and condensate in the ground state, or they form pairs. Pairs occur at strong interactions, e.g., on the chequerboard lattice. The general mechanism behind this phenomenon is discussed.