  A generalized description of entanglement and quantum correlation properties
constraining internal degrees of freedom of Dirac(-like) structures driven by
arbitrary Poincar\'e classes of external field potentials is proposed. The role
of (pseudo)scalar, (pseudo)vector and tensor interactions in
producing/destroying intrinsic quantum correlations for $\mbox{SU}(2) \otimes
\mbox{SU}(2)$ bi-spinor structures is discussed in terms of generic coupling
constants. By using a suitable ansatz to obtain the Dirac Hamiltonian
eigenspinor structure of time-independent solutions of the associated Liouville
equation, the quantum entanglement, via concurrence, and quantum correlations,
via geometric discord, are computed for several combinations of well-defined
Poincar\'e classes of Dirac potentials. Besides its inherent formal structure,
our results setup a framework which can be enlarged as to include localization
effects and to map quantum correlation effects into Dirac-like systems which
describe low-energy excitations of graphene and trapped ions.
