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

Abstract

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.