Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions

Understand

We report on Hybrid-Monte-Carlo simulations of the tight-binding model with long-range Coulomb interactions for the electronic properties of graphene.

• We investigate the spontaneous breaking of sublattice symmetry corresponding to a transition from the semimetal to an antiferromagnetic insulating phase.
• Our short-range interactions thereby include the partial screening due to electrons in higher energy states from ab initio calculations based on the constrained random phase approximation [T.O.Wehling {\it et al.}, Phys.Rev.Lett.{\bf 106}, 236805 (2011)].
• In contrast to a similar previous Monte-Carlo study [M.V.Ulybyshev {\it et al.}, Phys.Rev.Lett.{\bf 111}, 056801 (2013)] we also include a phenomenological model which describes the transition to the unscreened bare Coulomb interactions of graphene at half filling in the long-wavelength limit.