Condensation of Bosons in Flat Bands: From Frustrated Magnets to Cold Atoms

At low enough temperatures, weakly interacting bosons condense and a macroscopic number of particles occupy one single-particle state. Here we investigate the properties of a bosonic system in a flat band, where no well-defined minimum energy state facilitates such a condensation. In particular, we study the low-density phases of bosons on two geometrically frustrated lattices, the kagome lattice and the sawtooth chain.  We characterize the low-energy physics which is completely dominated by the interactions and comment on its experimental relevance to spin-1 antiferromagnets and cold-atoms in artificial lattice potentials.