Quantum lattice models for the excited-state spectra of graphene-based systems . Exact diagonalization results for the half-filled Hubbard model .

The theoretical investigation of the interplay between geometrical and electronic properties in graphene-based systems such as single-walled carbon nanotubes (SWNTs) and graphene nanoribbons (GNRs) is crucial both for the advance of condensed matter physics in low-dimensional systems and the development of new opto-electronic devices. In this talk I will first survey the basics concepts needed to understand the electronic properties of SWNTs and GNRs in the framework of the tight-binding model; electronic band structures and optical selection rules in GNRs for both longitudinally and transversely polarized photons will be discussed and compared to those known for SWNTs. Then I'll briefly review some experimental evidence of the failure of single-particle approximation revealing the presence of electronic correlation effects in SWNTs. The exact diagonalization (ED) method of the Hubbard model will be presented as a full many-body approach going beyond perturbative and mean-field techniques for elucidating the excitonic fine structure of these systems. I will show how the use of appropriate quantum lattice models with a well definite set of boundary conditions allows to capture the main features of the excited state properties of these systems and their size dependence in the low-intermediate correlation regime.