Phase diagram of strongly attractive p-orbital fermions on optical lattices

•We study strongly attractive p-orbital fermions on optical lattices.•We map the system Hamiltonian to an effective spin Hamiltonian.•We use a variational approach and a linear spin wave theory to map the phase diagram.•The results can be experimentally tested using cold atomic systems.

We examine a system of doubly degenerate p-orbital polarized fermions on a two-dimensional square lattice with a strong on-site interaction. We consider the system density at the half filling limit and tackle the strong attractive interaction using a perturbation theory. We treat the four-site square plaquette interaction term generated from the directional tunneling dependence of p-orbitals using the fourth order in perturbation theory. We map the strong coupling particle Hamiltonian into an effective spin-Hamiltonian and then use a variational mean field approach and a linear spin-wave theory to study the phase diagram. Further, we discuss the experimental signatures of these phases within the context of current cold-atom experimental techniques.