Order-N implementation of exact exchange in extended systems

Exact (Hartree Fock) exchange is needed to overcome some of the limitations of local and semilocal approximations of density functional theory (DFT). So far, however, computational cost has limited the use of exact exchange in plane wave calculations for extended systems. We show that this difficulty can be overcome by performing a unitary transformation from Bloch to Maximally Localized Wannier functions in combination with an efficient technique to compute real space Coulomb integrals. The resulting scheme scales linearly with system size. We validate the scheme with representative applications.