Bosons in flat band lattices: Kagome and beyond

We provide a scheme to investigate and identify systems with flat bands, like the Kagome and Lieb lattices, and address the sensitivity of the flat bands to the hopping parameters. A unique feature of the energy spectrum of a flat-band system, such as the Kagome lattice, is the parabolic band touching of the flat band and a dispersing one at the Γ-point. When the lattice sites are populated by hard core spins, it is known that the ground-state energy is determined solely by the occupancy of the flat-band up to a filling fraction of ν=1/9. Beyond this point, the parabolic band at higher energies begins to populate, leading to the physics of Bose-Einstein condensation. Upon fermionizing such a system, we can treat the bosonic excitations as fermions interacting with a Chern-Simons(CS) gauge field. These fermions have an interesting property that they occupy the flat-band up to ν=1/3. We investigate the precise role played by CS-gauge field which connects the fermionic ν=1/3 state to the bosonic ν=1/9 state. In the process we also address the formation of `moats’ in the electronic structure of such systems that prevents the formation of a condensate (which leads to a spin-liquid behavior).