We study single-particle properties of a spinless $p$-band correlated fermionic gas in an optical lattice by means of a variational cluster approach (VCA). The single-particle spectral function is almost flat at half filling and develops a strongly dispersive behavior at lower fillings. The competition between different orbital orderings is studied as a function of filling. We observe that an “antiferromagnetic” orbital order develops at half filling and is destroyed by doping the system evolving into a disordered orbital state. At low-filling limit, we discuss the possibility of “ferromagnetic” orbital order by complementing the VCA result with observations based on a trial wave function. We also study the behavior of the momentum distribution for different values of the on-site interaction. Finally, we introduce an integration contour in the complex plane which allows to efficiently carry out Matsubara frequency sums.

• Received 2 February 2009

DOI:https://doi.org/10.1103/PhysRevB.79.245109