Properties of Definite Bethe–Salpeter Eigenvalue Problems

  • Meiyue Shao
  • Chao Yang
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 117)


The Bethe–Salpeter eigenvalue problem is solved in condense matter physics to estimate the absorption spectrum of solids. It is a structured eigenvalue problem. Its special structure appears in other approaches for studying electron excitation in molecules or solids also. When the Bethe–Salpeter Hamiltonian matrix is definite, the corresponding eigenvalue problem can be reduced to a symmetric eigenvalue problem. However, its special structure leads to a number of interesting spectral properties. We describe these properties that are crucial for developing efficient and reliable numerical algorithms for solving this class of problems.



The authors thank Ren-Cang Li for helpful discussions. Support for this work was provided through Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Lawrence Berkeley National LaboratoryBerkeleyUSA

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