Coulomb Control of CHSH Nonlocality, EPR Steering and Entanglement in a Graphene-Inspired Fermi-Hubbard Dimer

We study the dynamics of quantum nonlocality in a graphene-inspired two-carbon-atom Fermi-Hubbard system. Three measures of quantum correlation are examined. These are the entanglement of formation, the Einstein-Podolsky-Rosen steering, and the violation of the CHSH inequality. The system is modelled by the extended Hubbard Hamiltonian with on-site and nearest-neighbour Coulomb interactions, and intrinsic decoherence is described by Milburn's model. The half-filled sector, the two-qubit encoding and the initial state are specified. The two Coulomb energies act through their difference alone. This difference fixes a fast timescale set by the charge gap and a slow timescale set by the superexchange splitting. The level of correlation that the system reaches is fixed by the preparation. Intrinsic decoherence removes the fast component before the slow one, so the lifetime of the nonlocal correlations grows as the difference of the Coulomb energies grows. The entanglement of formation survives after the nonlocal measures have vanished.