Inhomogeneous phases of repulsive fermions in cubic lattices

We present a fully self-consistent mean-field study of the inhomogeneous phases in the three-dimensional Hubbard model as the density deviates from half-filling. As the interaction U increases at fixed density, there is a transition from a uniform Fermi liquid to an inhomogeneous metallic phase characterized by a spin density wave along the [001] direction. Upon further increase of U the system undergoes a discontinuous transition to an insulating phase with a spin density wave along the [111] direction. We determine the evolution of the modulation wavelength of the spin density wave as a function of U and density, and discuss signature in the momentum distribution that are relevant to optical lattice experiments. Crossover from two- to three-dimensions is also studied.