  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, we are able to successfully confront 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
and higher-order perturbative corrections beyond RPA for the quantitative
description of the experimental data for the Fermi velocity renormalization in
suspended graphene.
