Imaginary time, shredded propagator method for large-scale GW calculations

The GW method is one of the most accurate ab initio methods for the prediction of electronic band structures. Despite its power, the GW method is not routinely applied to large scale materials physics or chemistry problems due to its unfavorable computational scaling: standard implementations scale as O(N⁴) where N is the number of electrons in the system. To develop large-scale GW software, we have implemented algorithms that work in real space for the canonical plane-wave pseudopotential approach to electronic structure calculations. One benefit is that the real-space polarizability matrix method requires substantially fewer fast Fourier transforms compared to the standard reciprocal space methods. In addition, use of real-space allows us to create a cubic scaling algorithm which utilizes Laplace transform over imaginary time with Gauss-Laguerre quadrature. The use of energy windows maximizes the efficiency of the quadrature integration. For the GW self-energy, we are also able to use energy windows and quadrature to achieve cubic scaling. In this presentation, we will describe these methods, their accuracies and their efficiencies compared to other available GW methods.