Fully self-consistent finite-temperature GW in Gaussian Bloch orbitals for solids

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 selfenergy 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 scGW 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 scGW for ab initio correlated material simulations and provides a sound starting point for embedding methods built on top of GW.