  We extend Nuclear Lattice Effective Field Theory (NLEFT) to medium-mass
nuclei, and present results for the ground states of alpha nuclei from $^4$He
to $^{28}$Si, calculated up to next-to-next-to-leading order (NNLO) in the EFT
expansion. This computational advance is made possible by extrapolations of
lattice data using multiple initial and final states. For our soft two-nucleon
interaction, we find that the overall contribution from multi-nucleon forces
must change sign from attractive to repulsive with increasing nucleon number.
This effect is not produced by three-nucleon forces at NNLO, but it can be
approximated by an effective four-nucleon interaction. We discuss the
convergence of the EFT expansion and the broad significance of our findings for
future ab initio calculations.
