In this work, 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 graphics processing units, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc $GW$ for ab initio correlated material simulations and provides a sound starting point for embedding methods built on top of $GW$.
@article{osti_2422080,
author = {Yeh, Chia-Nan and Iskakov, Sergei and Zgid, Dominika and Gull, Emanuel},
title = {Fully self-consistent finite-temperature $GW$ in Gaussian Bloch orbitals for solids},
annote = {In this work, 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 graphics processing units, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc $GW$ for ab initio correlated material simulations and provides a sound starting point for embedding methods built on top of $GW$.},
doi = {10.1103/physrevb.106.235104},
url = {https://www.osti.gov/biblio/2422080},
journal = {Physical Review. B},
issn = {ISSN 2469-9950},
number = {23},
volume = {106},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2022},
month = {12}}
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); University of California, Santa Barbara, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Basic Energy Sciences (BES)
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 200, Issue 1063, p. 542-554https://doi.org/10.1098/rspa.1950.0036