Deterministic and Faster GW Calculations with a Reduced Number of Valence States: O(N2 ln N) Scaling in the Plane-Waves Formalism

We introduce a method for reducing the number of valence states entering the calculation of screened the Coulomb interaction W in GW calculations. In this way, denoting with N the generic size of a system, the computational cost is brought from the typical O(N4) to the more favorable O(N2 ln N). The method becomes effective for large model structures. For enhancing the potentialities of our scheme, we combined it with a linear-response GW approach, which can exploit the symmetries of the simulation cell in direct space. We registered quadratic scaling up to more than thousand atoms with an almost 10-fold speed-up with respect to a standard implementation. Our scheme can be extended to any linear response calculation.