  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.
