Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene and benzene

To understand how nonlocal Coulomb interactions affect the phase diagram of correlated electron materials, we report on a method to approximate a correlated lattice model with nonlocal interactions by an effective Hubbard model with on-site interactions U* only. The effective model is defined by the Peierls-Feynman-Bogoliubov variational principle. We find that the local part of the interaction U is reduced according to U*=U-V', where V' is a weighted average of nonlocal interactions. For graphene, silicene and benzene we show that the nonlocal Coulomb interaction can decrease the effective local interaction by more than a factor of 2 in a wide doping range.