Graphene as a lattice field theory

We report on the status of ongoing ab-initio simulations of the electronic properties of mono-layer graphene within the tight-binding description. Hereby we employ standard methods of lattice field theory, similar to those used in simulations of quantum chromodynamics. We present results concerning the semimetal-insulator phase-transition, which is analogous to chiral symmetry-breaking in strongly interacting field theories, and concerning the topological neck-disrupting Lifshitz transition, which occurs at finite electron number-density.