  Electron correlation in graphene is unique because of the interplay of the
Dirac cone dispersion of $\pi$ electrons with long range Coulomb interaction.
The random phase approximation predicts no metallic screening at long distance
and low energy because of the zero density of states at Fermi level, so one
might expect that graphene should be a poorly screened system. However,
empirically graphene is a weakly interacting semimetal, which leads to the
question of how electron correlations take place in graphene at different
length scales. We address this question by computing the equal time and dynamic
structure factor $S(\vec q)$ and $S(\vec q, \omega)$ of freestanding graphene
using {\it ab-initio} fixed-node diffusion Monte Carlo and the random phase
approximation. We find that the $\sigma$ electrons contribute strongly to
$S(\vec q,\omega)$ for relevant experimental values of $\omega$ even at
distances up to around 80 \AA. These findings illustrate how the emergent
physics from underlying Coulomb interactions results in the observed weakly
correlated semimetal.

Materials Science