Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids

TL;DR

This paper develops a fully self-consistent finite-temperature GW method using Gaussian Bloch orbitals, enabling accurate band gap calculations for solids without analytical continuation, and demonstrates scalable GPU implementation for large-scale materials simulations.

Contribution

It introduces a novel fully self-consistent finite-temperature GW algorithm in Gaussian orbitals, with GPU acceleration and validation against existing methods.

Findings

Accurate band gap calculations for semiconductors and insulators.

Agreement with other finite-temperature scGW implementations.

Scalable GPU-based computations for large supercomputing resources.

Abstract

We present algorithmic and implementation details for the fully self-consistent finite-temperature $GW$ method in Gaussian Bloch orbitals for solids. Our implementation is based on the finite-temperature Green's function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of the self-energy are explicitly evaluated. The method is tested by evaluating the band gaps of selected semiconductors and insulators. We show agreement with other, differently formulated finite-temperature sc$GW$ implementations when finite-size corrections and basis set errors are taken into account. By migrating computationally intensive calculations to GPUs, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc$GW$ for $\emph{ab initio}$ correlated materials simulations and provides a sound starting point for embedding methods built on top of $GW$.