Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band.

The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure quantity derived solely from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behavior of the superfluid weight of high-T_{c} superconductors.

Topological Phase Transitions in the Repulsively Interacting Haldane-Hubbard Model.

Using dynamical mean-field theory and exact diagonalization we study the phase diagram of the repulsive Haldane-Hubbard model, varying the interaction strength and the sublattice potential difference. In addition to the quantum Hall phase with Chern number C=2 and the band insulator with C=0 present already in the noninteracting model, the system also exhibits a C=0 Mott insulating phase, and a C=1 quantum Hall phase. We explain the latter phase by a spontaneous symmetry breaking where one of the spin components is in the Hall state and the other in the band insulating state.