Henneke, F. and Lin, L. and Vorwerk, C. and Draxl, C. and Klein, R. and Yang, C.
(2020)
*Fast Optical Absorption Spectra Calculations for Periodic Solid State Systems.*
Communications in Applied Mathematics and Computational Science, 15
(1).
pp. 89-113.

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Official URL: https://msp.org/camcos/2020/15-1/p04.xhtml

## Abstract

We present a method to construct an efficient approximation to the bare exchange andscreened direct interaction kernels of the Bethe-Salpeter Hamiltonian for periodic solid state systemsvia the interpolative separable density fitting technique. We show that the cost of constructing the approximate Bethe-Salpeter Hamiltonian scales nearly optimally asO(Nk) with respect to thenumber of samples in the Brillouin zoneNk. In addition, we show that the cost for applying the Bethe-Salpeter Hamiltonian to a vector scales asO(NklogNk). Therefore the optical absorption spectrum,as well as selected excitation energies can be efficiently computed via iterative methods such as the Lanczos method. This is a significant reduction from theO(N2k) andO(N3k) scaling associated with a brute force approach for constructing the Hamiltonian and diagonalizing the Hamiltonian respectively. We demonstrate the efficiency and accuracy of this approach with both one-dimensionalmodel problems and three-dimensional real materials (graphene and diamond). For the diamond system withNk= 2197, it takes 6 hours to assemble the Bethe-Salpeter Hamiltonian and 4 hours to fully diagonalize the Hamiltonian using 169 cores when the brute force approach is used. The new method takes less than 3 minutes to set up the Hamiltonian and 24 minutes to compute the absorption spectrum on a single core.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Bethe–Salpeter equation, interpolative separable density fitting, optical absorptionfunction |

Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group |

ID Code: | 2422 |

Deposited By: | Ulrike Eickers |

Deposited On: | 02 Apr 2020 07:12 |

Last Modified: | 15 Sep 2020 05:04 |

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