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Optical Response and Ground State of Graphene

The optical response and the ground state of graphene and graphene-like systems are determined self-consistently. Deriving equations of motion for the basic variables, graphene Bloch equations are introduced and combined with a variational Ansatz for the ground state. Within the Hartree--Fock approximation, this approach reproduces the gap equation for the ground state. The results show that the Coulomb interaction drastically influences the optical response of graphene and introduces an extremely sensitive dependency on the dielectric environment via screening. Regarding the effective fine-structure constant as control parameter, a transition from a semimetal to an excitonic insulator is predicted as soon as the effective graphene fine-structure constant exceeds a value of roughly 0.5. Above this critical value, the computed optical spectra exhibit a pseudogap and several bright $p$-like excitonic resonances.