Monte-Carlo study of quasiparticle dispersion relation in monolayer graphene

The density of electronic one-particle states in monolayer graphene is studied by performing the Hybrid Monte-Carlo simulations of the tight-binding model for electrons on the pi orbitals of carbon atoms which make up the graphene lattice. Density of states is approximated as a derivative of the number of particles over the chemical potential at sufficiently small temperature. Simulations are performed in the partially quenched approximation, in which virtual particles and holes have zero chemical potential. It is found that the Van Hove singularity becomes much sharper than in the free tight-binding model. Simulation results also suggest that the Fermi velocity increases with interaction strength up to the transition to the phase with spontaneously broken chiral symmetry.