Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical Lattices

In this work we study ultracold Fermions confined in a two-dimensional optical lattice and we explore the Mott-insulator transition with the Fermi-Hubbard model. On the basis of a mean-field approach, we study the phase diagrams in the presence of a harmonic trapping potential. Local Mott-insulator phases are shown to be generally situated in the center of the trap and correspond to a vanishing variance of the local density. We then study the effects induced by rotation on the Mott-insulator phase transition. In particular, we show that the phase boundary reproduces the edge of the Hofstadter butterfly.