# Properties of definite Bethe–Salpeter eigenvalue problems

## Abstract

The Bethe-Salpeter eigenvalue problem is solved in condensed 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.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1439213

- DOE Contract Number:
- AC02-05CH11231

- Resource Type:
- Conference

- Resource Relation:
- Conference: International Workshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing. EPASA 2015, Tsukuba (Japan), Sep 2015; Related Information: Part of the Lecture Notes in Computational Science and Engineering Series, 2017

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Shao, Meiyue, and Yang, Chao.
```*Properties of definite Bethe–Salpeter eigenvalue problems*. United States: N. p., 2017.
Web. doi:10.1007/978-3-319-62426-6_7.

```
Shao, Meiyue, & Yang, Chao.
```*Properties of definite Bethe–Salpeter eigenvalue problems*. United States. doi:10.1007/978-3-319-62426-6_7.

```
Shao, Meiyue, and Yang, Chao. Sun .
"Properties of definite Bethe–Salpeter eigenvalue problems". United States. doi:10.1007/978-3-319-62426-6_7. https://www.osti.gov/servlets/purl/1439213.
```

```
@article{osti_1439213,
```

title = {Properties of definite Bethe–Salpeter eigenvalue problems},

author = {Shao, Meiyue and Yang, Chao},

abstractNote = {The Bethe-Salpeter eigenvalue problem is solved in condensed 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.},

doi = {10.1007/978-3-319-62426-6_7},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2017},

month = {1}

}

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