Many-body effects in graphene

A huge recent progress in the sample quality makes many-body effects in electron spectrum of graphene near neutrality point observable. Model approaches for the Dirac electrons with Coulomb interaction were intensively developed in the last ten years. I am going to focus, rather, on materials-science aspects of the problem, including first-principles calculations of effective Coulomb interaction and its further mapping on the optimal Hubbard model; I will discuss also a problem of sp-electron magnetism in graphene and other graphitic systems.I will present also the results of Quantum Monte Carlo simulations for pristine and defected graphene. They demonstrate a crucial importance of realistic interelectron interaction potential for the phase diagram of isolated graphene and give the final answer in a long and controversial discussion on many-body renormalization of optical conductivity in graphene. It turns out that this renormalization is very weak or absent.As an example of unusual many-body effects in graphene I will discuss also the renormalization of ballistic minimal conductivity by the electron-electron Coulomb interaction.