  We apply the quasi-particle self-consistent GW (QSGW) approximation to some
of the iron pnictide and chalcogenide superconductors. We compute Fermi
surfaces and density of states, and find excellent agreement with experiment,
substantially improving over standard band-structure methods. Analyzing the
QSGW self-energy we discuss non-local and dynamic contributions to effective
masses. We present evidence that the two contributions are mostly separable,
since the quasi-particle weight is found to be essentially independent of
momentum. The main effect of non locality is captured by the static but
non-local QSGW effective potential. Moreover, these non-local self-energy
corrections, absent in e.g. dynamical mean field theory (DMFT), can be
relatively large. We show, on the other hand, that QSGW only partially accounts
for dynamic renormalizations at low energies. These findings suggest that QSGW
combined with DMFT will capture most of the many-body physics in the iron
pnictides and chalcogenides.
