Low Rank Approximation in Electron Excitation Calculations - IPAM at UCLA

Explore a 42-minute lecture on low rank approximation techniques in electron excitation calculations, presented by Chao Yang from Lawrence Berkeley National Laboratory at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Delve into the practical approach of using Kohn-Sham density functional theory for ground state calculations, followed by solving Dyson's equation for Green's functions. Discover how the interpolative separable density fitting (ISDF) technique can significantly reduce computational costs in post-DFT calculations. Examine the effectiveness of low rank approximation in these calculations and learn about the accuracy and efficiency of this approach. The lecture covers topics such as the quantum many-body problem, Lehmann representation, BSE Hamiltonian, integral computation, ISDF implementation, and its application to both periodic and non-periodic systems.

LOW RANK APPROXIMATION IN ELECTRON EXCITATION CALCULATIONS
Outline
Quantum many-body problem and electron excitation
Lehmann representation
BSE Hamiltonian
Integral computation: the matrix view
Interpolative Separable Density Fitting
Computing ISDF
Take advantage of separability
Choosing interpolation points
Extended (periodic) systems
ISDF for periodic systems
Examples (non-periodic systems)
The ranks of pair product basis (CO)
Accuracy vs rank truncation (Six)
Optical absorption spectrum
ISDF Efficiency