Spinor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math> /Bethe-Salpeter calculations in BerkeleyGW: Implementation, symmetries, benchmarking, and performance

Computing the $GW$ quasiparticle bandstructure and Bethe-Salpeter Equation (BSE) absorption spectra for materials with spin-orbit coupling has commonly been done by treating corrections as separate perturbations to density-functional theory. However, accurate treatment of strong often requires a fully relativistic approach using spinor wavefunctions in Kohn-Sham equation $GW$/BSE. Such calculations have only recently become available, particular BSE. We implemented this plane-wave pseudopotential $GW$/BSE code BerkeleyGW, which is highly parallelized widely used electronic-structure community. present reference results bandstructures optical solids different strengths coupling, including Si, Ge, GaAs, GaSb, CdSe, Au, Bi$_2$Se$_3$. The calculated band gaps these systems are found agree experiment within few tens meV. spectrum GaSb fully-relativistic $GW$-BSE captures large splitting peaks spectrum. For Bi$_2$Se$_3$, we find drastic change low-energy compared that DFT, approximation correctly capturing parabolic nature valence conduction bands after off-diagonal self-energy matrix elements. detailed methodology, spatial symmetries spinors, comparison against other codes, performance spinless perturbative approaches SOC. This work aims spur further development methodology excited-state research software.