Deterministic and\nFaster GW Calculations with a Reduced\nNumber of Valence States: <i>O</i>(<i>N</i><sup>2</sup> ln <i>N</i>) Scaling in the Plane-Waves\nFormalism

We introduce a method for reducing the number of valence\nstates\nentering the calculation of screened the Coulomb interaction <i>W</i> in <i>GW</i> calculations. In this way, denoting\nwith <i>N</i> the generic size of a system, the computational\ncost is brought from the typical <i>O</i>(<i>N</i><sup>4</sup>) to the more favorable <i>O</i>(<i>N</i><sup>2</sup> ln <i>N</i>). The method becomes\neffective for large model structures. For enhancing the potentialities\nof our scheme, we combined it with a linear-response <i>GW</i> approach, which can exploit the symmetries of the simulation cell\nin direct space. We registered quadratic scaling up to more than thousand\natoms with an almost 10-fold speed-up with respect to a standard implementation.\nOur scheme can be extended to any linear response calculation.