  Recent experiments on twisted bilayer graphene show the urgent need for
establishing a low-energy lattice model for the system. We use the constrained
random phase approximation to study the interaction parameters of such models
taking into account screening from the moire bands left outside the model
space. Based on an atomic-scale tight-binding model, we develop a numerically
tractable approximation to the polarization function and study its behavior for
different twist angles. We find that the polarization has three different
momentum regimes. For small momenta, the polarization is quadratic, leading to
a linear dielectric function expected for a two-dimensional dielectric
material. For large momenta, the polarization becomes independent of the twist
angle and approaches that of uncoupled graphene layers. In the intermediate
momentum regime, the dependence on the twist-angle is strong. Close to the
largest magic angle the dielectric function peaks at a momentum of $~1/(4 \:
nm)$ attaining values of 25, meaning very strong screening at intermediate
distances. We also calculate the effective screened Coulomb interaction in real
space and give estimates for the on-site and extended interaction terms for the
recently developed hexagonal-lattice model. For free-standing TBG the effective
interaction decays slower than $1/r$ at intermediate distances $r$, while it
remains essentially unscreened at large enough $r$.
