Beyond the Tamm-Dancoff approximation for extended systems using exact diagonalization

Autor(en)

Tobias Sander, Emanuele Maggio, Georg Kresse

Abstrakt

Linear optical properties can be accurately calculated using the Bethe-Salpeter equation. After introducing a suitable product basis for the electron-hole pairs, the Bethe-Salpeter equation is usually recast into a complex non-Hermitian eigenvalue problem that is difficult to solve using standard eigenvalue solvers. In solid-state physics, it is therefore common practice to neglect the problematic coupling between the positive-and negative-frequency branches, reducing the problem to a Hermitian eigenvalue problem [Tamm-Dancoff approximation (TDA)]. We use time-inversion symmetry to recast the full problem into a quadratic Hermitian eigenvalue problem, which can be solved routinely using standard eigenvalue solvers even at a finite wave vector q. This allows us to access the importance of the coupling between the positive- and negative-frequency branch for prototypical solids. As a starting point for the Bethe-Salpeter calculations, we use self-consistent Green's-function methods (GW), making the present scheme entirely ab initio. We calculate the optical spectra of carbon (C), silicon (Si), lithium fluoride (LiF), and the cyclic dimer Li2F2 and discuss why the differences between the TDA and the full solution are tiny. However, at finite momentum transfer q, significant differences between the TDA and our exact treatment are found. The origin of these differences is explained.

Organisation(en)

Computergestützte Materialphysik

Journal

Physical Review B

Band

92

Anzahl der Seiten

14

ISSN

1098-0121

DOI

https://doi.org/10.1103/PhysRevB.92.045209

Publikationsdatum

07-2015

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik, 103036 Theoretische Physik, 103015 Kondensierte Materie, 103009 Festkörperphysik

Schlagwörter

ASJC Scopus Sachgebiete

Electronic, Optical and Magnetic Materials, Condensed Matter Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/7a2eff20-b752-4537-9b2a-4ad191b43f01