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.
Mikhail Katsnelson finished Ural State University (Sverdlovsk, USSR – now Ekaterinburg) in 1977 and received PhD in 1980; for many years (1977-2001) he was working in the Institute of Metal Physics in Ekaterinburg (the last position – head of the group of Quantum Theory of Metals). He became the youngest physicist - Doctor of Sciences in the USSR (1985) and received Lenin Komsomol Prize (State Prize for young researchers, 1988). After working for several years as a visiting professor in Uppsala University (Sweden) he became (in 2004) professor of theoretical physics and head of the group of Theory of Condensed Matter in Radboud University (Nijmegen, Netherlands). He is one of the most active and most recognized theoretical physicists now, with more than 80,000 citations according to Google Scholar (h=98). Prof. Katsnelson works in many fields of physics, from foundations of quantum mechanics to applications of statistical physics in biology. His best known achievements are in the theory of graphene, magnetism and strongly correlated systems. He is awarded by Spinoza Prize (top scientific award in Netherlands), Hamburg Prize in Theoretical Physics and by Royal decoration as a Knight of the Order of the Netherlands Lion. Prof. Katsnelson is elected member of Royal Netherlands Academy of Arts and Sciences, Academia Europaea and Royal Society of Sciencesat Uppsala and honorary doctor of Uppsala University.