with the band structure calculations and with isotropic $s$-wave superconducting gaps [@prichard]. Therefore, at first sight it may appear that antiferromagnetism in the iron-based materials originates from FS nesting of itinerant electrons, superconductivity must have a $s^{\pm}$-wave symmetry for related reasons, and electron correlations or local moments do not play an important role for magnetism and superconductivity [@mazin2011n].

However, although the parent compounds of iron pnictide superconductors have metallic ground states consistent with band structure calculations, there are reasons to believe that electron correlations could be sufficiently strong to produce an “incipient” Mott physics [@si2008; @qmsi09], where local moments are as important as itinerant electrons for magnetic, transport, and superconducting properties in these materials [@cfang; @cxu]. In fact, the $s^{\pm}$ pairing symmetry is also naturally derived in multi-orbital $t-J$-type models [@seo2008; @Fang2011] and recent diagonalization calculations [@nicholson11] have shown that the AF state, as well as the $A_{1g}$ $s$-wave pairing state, evolve smoothly from weak to strong coupling, suggesting that the physics of the pnictides could also be rationalized based on short length scale concepts not rooted in weak-coupling nesting. After all, in the context of the copper oxide superconductors, weak coupling studies of the one-orbital Hubbard model also led 