Vol. 15, No. 1, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 15, Issue 1
Volume 14, Issue 2
Volume 14, Issue 1
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 1
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 1
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Author Index
To Appear
 
Other MSP Journals
Fast optical absorption spectra calculations for periodic solid state systems

Felix Henneke, Lin Lin, Christian Vorwerk, Claudia Draxl, Rupert Klein and Chao Yang

Vol. 15 (2020), No. 1, 89–113
Abstract

We present a method to construct an efficient approximation to the bare exchange and screened direct interaction kernels of the Bethe–Salpeter Hamiltonian for periodic solid state systems via the interpolative separable density fitting technique. We show that the cost of constructing the approximate Bethe–Salpeter Hamiltonian can be reduced to nearly optimal as 𝒪(Nk) with respect to the number of samples in the Brillouin zone Nk for the first time. In addition, we show that the cost for applying the Bethe–Salpeter Hamiltonian to a vector scales as 𝒪(Nk logNk). 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 the 𝒪(Nk2) and 𝒪(Nk3) 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-dimensional model problems and three-dimensional real materials (graphene and diamond). For the diamond system with Nk = 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.

Keywords
Bethe–Salpeter equation, interpolative separable density fitting, optical absorption function
Mathematical Subject Classification 2010
Primary: 65F15, 65Z05
Milestones
Received: 10 December 2019
Accepted: 3 March 2020
Published: 3 June 2020
Authors
Felix Henneke
Institut für Mathematik
Freie Universität Berlin
Berlin
Germany
Lin Lin
Department of Mathematics
University of California, Berkeley
Berkeley, CA
United States
Computational Research Division
Lawrence Berkeley National Laboratory
Berkeley, CA
United States
Christian Vorwerk
Institut für Physik
IRIS Adlershof
Humboldt-Universität zu Berlin
Berlin
Germany
Claudia Draxl
Institut für Physik
IRIS Adlershof
Humboldt-Universität zu Berlin
Berlin
Germany
Rupert Klein
Institut für Mathematik
Freie Universität Berlin
Berlin
Germany
Chao Yang
Computational Research Division
Lawrence Berkeley National Laboratory
Berkeley, CA
United States