We derive and analyze the $f$-sum rule for a two-dimensional system of interacting electrons whose behavior is described by the Dirac equation. We apply the sum rule to analyze the spectral weight transfer in graphene within different approximations discussed in the literature. We find that the sum rule is generically dominated by interband transitions while other excitations produce subleading behavior. The $f$-sum rule provides strong constraints for theories of interacting electrons in graphene.

• Received 13 June 2008

DOI:https://doi.org/10.1103/PhysRevB.78.075410