| תקציר: | On certain lattices interference effects lead to completely flat Bloch bands. Such flat bands host equally interesting physics for itinerant particles as their counter part, frustrated magnets, for localized spins. I will review the connection between the behavior of such itinerant particles and the physics of localized spins. On the example of a simple one dimensional model I illustrate how already weak interactions can lead to a number of exotic quantum phases. I discuss the relevance of our results for various systems including ultra-cold atomic gases in optical lattices, frustrated magnets in a strong magnetic field, and spin-ful bosons with Rashba interactions. |