Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

TL;DR

This study evaluates the accuracy of diagonal G and subspace W approximations in fully self-consistent GW calculations for bulk semiconductors, finding they are highly accurate with less than 1.7% bandgap difference from full matrix methods.

Contribution

It systematically compares diagonal G and subspace W approximations with full matrix sc-GW, validating their use in reducing computational cost while maintaining accuracy.

Findings

Differences in quasiparticle bandgap are mostly less than 1.7%.

Approximations are validated for use in higher-order corrections.

Low-rank approximations significantly reduce computational demands.

Abstract

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. The routinely used single-shot GW-approximation (G0W0) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth to check how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of non-interacting G such that only diagonal elements are retained, whereas, the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle bandgap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7% that validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms like the vertex correction.