Deterministic and Faster GW Calculations with a Reduced Number of Valence States: O(N 2 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(N 4) to the more favorable O(N 2 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.