  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.
