I will describe the phase diagram of a three orbital model
in the presence of e-e interaction, including the Hund’s coupling and
a local Spin Orbit Coupling (SOC), obtained through
Dynamical Mean-Field Theory and a state of the art ED solver for
the impurity problem. The interplay between the full rotational
invariant Kanamori interaction and band-structure features due
to SOC will be discussed alongside with the various emergent phases.
This study address several recent issues in the field of
correlated spin-orbital metals and Mott insulators, including, e.g., the
relativistic Mott insulating state of iridates.