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The GW approximation is a well-known method to improve electronic structurepredictions calculated within density functional theory. In this work, we haveimplemented a computationally efficient GW approach that calculates centralproperties within the Matsubara-time domain using the modified version of Elk,the full-potential linearized augmented plane wave (FP-LAPW) package.Continuous-pole expansion (CPE), a recently proposed analytic continuationmethod, has been incorporated and compared to the widely used Padeapproximation. Full crystal symmetry has been employed for computationalspeedup. We have applied our approach to 18 well-studiedsemiconductors/insulators that cover a wide range of band gaps computed at thelevels of single-shot G0W0, partially self-consistent GW0, and fullyself-consistent GW (scGW). Our calculations show that G0W0 leads to band gapsthat agree well with experiment for the case of simple s-p electron systems,whereas scGW is required for improving the band gaps in 3-d electron systems.In addition, GW0 almost always predicts larger band gap values compared toscGW, likely due to the substantial underestimation of screening effects. Boththe CPE method and Pade approximation lead to similar band gaps for mostsystems except strontium titantate, suggesting further investigation into thelatter approximation is necessary for strongly correlated systems. Our computedband gaps serve as important benchmarks for the accuracy of the Matsubara-timeGW approach.

All-electron self-consistent GW in the Matsubara-time domain: implementation and benchmarks of semiconductors and insulators