We introduce and study an extended "t-U-J" two-orbital model for the pnictides that includes Heisenberg terms deduced from the strong coupling expansion. Including these J terms explicitly allows us to enhance the strength of the (π,0)-(0,π) spin order which favors the presence of tightly bound pairing states even in the small clusters that are here exactly diagonalized. The A(1g) and B(2g) pairing symmetries are found to compete in the realistic spin-ordered and metallic regime. The dynamical pairing susceptibility additionally unveils low-lying B(1g) states, suggesting that small changes in parameters may render any of the three channels stable.

To understand the role that degeneracy, hybridization, and nesting play in the magnetic and pairing properties of multiorbital Hubbard models we here study numerically two types of two-orbital models, both with holelike and electron-like Fermi surfaces (FS's) that are related by nesting vectors (π,0) and (0,π ). In one case the bands that determine the FS's arise from strongly hybridized degenerate d xz and d yz orbitals, while in the other the two bands are determined by nondegenerate and nonhybridized s-like orbitals. Using a variety of techniques, in the weak-coupling regime it is shown that only the model with hybridized bands develops metallic magnetic order, while the other model exhibits an ordered excitonic orbital-transverse spin state that is insulating and does not have a local magnetization. However, both models display similar insulating magnetic stripe ordering in the strong-coupling limit. These results indicate that nesting is a necessary but not sufficient condition for the development of ordered states with finite local magnetization in multiorbital Hubbard systems; the additional ingredient appears to be that the nested portions of the bands need to have the same orbital flavor. This condition can be achieved via strong hybridization of the orbitals in weak coupling or via the FS reconstruction induced by the Coulomb interactions in the strong-coupling regime. This effect also affects the pairing symmetry as demonstrated by the study of the dominant pairing channels for the two models.

The hole-doped ground state of a recently introduced extended "t-U -J" two-orbital Hubbard model for the Fe-based superconductors is studied via exact diagonalization methods on small clusters. Similarly as in the previously studied case of electron doping, A. Nicholson et al., Phys. Rev. Lett. 106 21702 (2011), upon hole doping it is observed that there are several competing pairing symmetries including A1g, B1g, and B2g. However, contrary to the electron-doped case, the ground state of the hole-doped state has pseudocrystal momentum k = (π, π) in the unfolded Brillouin zone. In the two Fe-atom per unit cell representation, this indicates that the ground state involves anti-bonding, rather than bonding, combinations of the orbitals of the two Fe atoms in the unit-cell. The lowest state with k = (0, 0) has only a slightly higher energy. These results indicate that this simple two-orbital model may be useful to capture some subtle aspects of the hole-doped pnictides since calculations for the five-orbital model have unveiled a hole pocket centered at M (k = (π, π)) in the unfolded Brillouin zone.