  We report results of large scale quantum Monte Carlo (QMC) simulations of
graphene. Using cutting-edge algorithmic improvements, we are able to consider
spatial volumes, corresponding to 20808 electrons, that allow us to access
energy scales of direct relevance to experiments. Using constrained random
phase approximation (cRPA) estimates of short ranged interactions combined with
a Coulomb tail akin to the vacuum, we are able to confront successfully
numerical and experimental estimates of the Fermi velocity renormalization.
These results and their comparison with perturbation theory not only show the
non-Fermi liquid character of graphene, but also prove the importance of
lattice-scale physics for the quantitative description of the experimental data
for the Fermi velocity renormalization in suspended graphene.
