Efficient dielectric matrix calculations using the Lanczos algorithm for fast many-body $G_0W_0$ implementations

@article{Janssen2014EfficientDM,
  title={Efficient dielectric matrix calculations using the Lanczos algorithm for fast many-body \$G\_0W\_0\$ implementations},
  author={Jonathan Laflamme Janssen and B. Rousseau and M. C{\^o}t{\'e}},
  journal={Physical Review B},
  year={2014},
  volume={91},
  pages={125120}
}
We present a $G_0W_0$ implementation that assesses the two major bottlenecks of traditional plane-waves implementations, the summations over conduction states and the inversion of the dielectric matrix, without introducing new approximations in the formalism. The first bottleneck is circumvented by converting the summations into Sternheimer equations. Then, the novel avenue of expressing the dielectric matrix in a Lanczos basis is developed, which reduces the matrix size by orders of magnitude… 
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