  Several recent works have proposed that electron-electron interactions in
bilayer graphene can be tuned with the help of external parameters, making it
possible to stabilize different fractional quantum Hall states. In these prior
works, phase diagrams were calculated based on a single Landau level
approximation. We go beyond this approximation and investigate the influence of
polarization effects and virtual interband transitions on the stability of
fractional quantum Hall states in bilayer graphene. We find that for realistic
values of the dielectric constant, the phase diagram is strongly modified by
these effects. We illustrate this by evaluating the region of stability of the
Pfaffian state.
