GW space-time method: Energy band gap of solid hydrogen

Abstract

We implement the $GW$ space-time method at finite temperatures, in which the Green's function $G$ and the screened Coulomb interaction $W$ are represented in the real space on a suitable mesh and in imaginary time in terms of Chebyshev polynomials, paying particular attention to controlling systematic errors of the representation. Having validated the technique by the canonical application to silicon and germanium, we apply it to the calculation of band gaps in hexagonal solid hydrogen with the bare Green's function obtained from density functional approximation and the interaction screened within the random phase approximation. The results, obtained from the asymptotic decay of the full Green's function without resorting to analytic continuation, suggest that the solid hydrogen above 150 GPa cannot adopt an orientationally ordered hexagonal-closed-pack structure due to its metallic behavior. The demonstrated ability of the method to store the full $G$ and $W$ functions in memory with sufficient accuracy is crucial for its subsequent extensions to include higher orders of the diagrammatic series by means of diagrammatic Monte Carlo algorithms.