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

TL;DR

This paper introduces a finite-temperature GW space-time method using real space and imaginary time representations, validated on silicon and germanium, and applied to study the band gap of solid hydrogen under high pressure.

Contribution

The paper develops and validates a GW space-time method at finite temperatures, enabling accurate band gap calculations without analytic continuation, and applies it to high-pressure solid hydrogen.

Findings

Solid hydrogen above 270 GPa likely does not adopt hcp structure.

The method accurately captures Green's function and W in real space and imaginary time.

Band gap calculations suggest structural insights into high-pressure 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 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 (RPA). The band gap results, obtained from the asymptotic decay of the full Green's function without resorting to analytic continuation, suggest that the solid hydrogen above 270 GPa can not adopt the hexagonal-closed-pack (hcp) structure. 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.