  Various intermetallic compounds harbor subtle electronic correlation effects.
To elucidate this fact for the Fe-Al system, we perform a realistic many-body
investigation based on the combination of density functional theory with
dynamical mean-field theory in a charge self-consistent manner. A better
characterization and understanding of the phase stability of bcc-based
D0$_3$-Fe$_3$Al through an improved description of the correlated charge
density and the magnetic-energy is achevied. Upon replacement of one Fe
sublattice by V, the Heusler compound Fe$_2$VAl is realized, known to display
bad-metal behavior and increased specific heat. We here document a charge-gap
opening at low temperatures in line with previous experimental work. The gap
structure does not match conventional band theory and is reminiscent of
(pseudo)gap charateristics in correlated oxides.
