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

Entanglement of Dirac bi-spinor states driven by Poincar\'e classes of $\mbox{SU}(2) \otimes \mbox{SU}(2)$ coupling potentials