  The modern semilocal exchange potential is an accurate and efficient
approximation to the exact exchange potential of density functional theory. We
tried to combine it with the dynamical mean-field theory to derive a new
first-principles many-body approach for studying correlated electronic
materials. As a paradigm, this approach was employed to investigate the
electronic structures and optical properties of strongly correlated ionic
insulator YbS. Compared to the standard density functional theory plus
dynamical mean-field theory which surprisingly failed to give an insulating
solution, the new approach correctly captured all of the important
characteristics of YbS. Not only an energy gap between a fully occupied Yb-4$f$
state and an unoccupied conduction band, but also an absence of Drude peak in
the optical conductivity $\sigma(\omega)$ were successfully reproduced.
