Linearized self-consistent quasiparticle GW method: Application to semiconductors and simple metals

We present a code implementing the linearized quasiparticle self-consistent GW method (LQSGW) in the LAPW basis. Our approach is based on the linearization of the self-energy around zero frequency which differs it from the existing implementations of the QSGW method. The linearization allows us to use Matsubara frequencies instead of working on the real axis. This results in efficiency gains by switching to the imaginary time representation in the same way as in the space time method. The all electron LAPW basis set eliminates the need for pseudopotentials. We discuss the advantages of our approach, such as its N^3 scaling with the system size N, as well as its shortcomings. We apply our approach to study the electronic properties of selected semiconductors, insulators, and simple metals and show that our code produces the results very close to the previously published QSGW data. Our implementation is a good platform for further many body diagrammatic resummations such as the vertex-corrected GW approach and the GW+DMFT method.本研究提出了一套基于线性缀加平面波（LAPW，Linear Augmented Plane Wave）基组的线性化准粒子自洽GW方法（LQSGW，linearized quasiparticle self-consistent GW method）的实现代码。我们的方法基于自能在零频处的线性化近似，这也是本方案与现有QSGW方法各类实现版本的核心差异所在。该线性化近似使得我们可以采用松原频率（Matsubara frequencies）进行计算，而非在实频轴上开展运算。通过与时空方法（space time method）一致的方式转换至虚时表象，该方案可实现计算效率的提升。全电子LAPW基组无需借助赝势即可完成计算。本文还讨论了该方法的优势与局限性，其中优势包括其计算开销随体系规模N呈现N³的标度关系。 我们将该方法应用于特定半导体、绝缘体与简单金属的电子性质研究，结果表明本代码的计算结果与已发表的QSGW数据高度吻合。本实现方案可作为进一步开展多体图解重求和研究的优良平台，例如顶点修正GW方法以及GW+动态平均场理论（GW+DMFT，Dynamic Mean Field Theory）等方向。