Space-Time Method for Ab Initio Calculations of Self-Energies and Dielectric Response Functions of Solids

We present a new method for efficient, accurate calculations of many-body properties of periodic systems. The main features are (i) use of a real-space/imaginary-time representation, (ii) avoidance of any model form for the screened interaction $W$, (iii) exact separation of $W$ and the self-energy $\Sigma$ into short- and long-ranged parts, and (iv) the use of novel analytical continuation techniques in the energy domain. The computer time scales approximately linearly with system size. We give results for jellium and silicon, including the spectral function of silicon obtained from the Dyson equation.