  The proton-proton fusion rate is calculated at low energy in a lattice
effective field theory (EFT) formulation. The strong and the Coulomb
interactions are treated non-perturbatively at leading order in the EFT. The
lattice results are shown to accurately describe the low energy cross section
within the validity of the theory at energies relevant to solar physics. In
prior work in the literature, Coulomb effects were generally not included in
non-perturbative lattice calculations. Work presented here is of general
interest in nuclear lattice EFT calculations that involve Coulomb effects at
low energy. It complements recent developments of the adiabatic projection
method for lattice calculations of nuclear reactions.
