Kadanoff-Baym approach to double-excitations in finite systems

TL;DR

This paper uses the Kadanoff-Baym approach to accurately compute excitation spectra in finite systems, highlighting the importance of time-nonlocal approximations for capturing double-excitations.

Contribution

It demonstrates that the second Born approximation effectively reproduces double-excitations in finite lattice systems, improving upon simpler methods like Hartree-Fock.

Findings

Hartree-Fock spectra can be incomplete

Second Born captures most double-excitations

Method respects frequency sum rule

Abstract

We benchmark many-body perturbation theory by studying neutral, as well as non-neutral, excitations of finite lattice systems. The neutral excitation spectra are obtained by time-propagating the Kadanoff-Baym equations in the Hartree-Fock and second Born approximations. Our method is equivalent to solving the Bethe-Salpeter equation with a high-level kernel while respecting self-consistently, which guarantees the fulfillment of a frequency sum rule. As a result, we find that a time-local method, such as Hartree-Fock, can give incomplete spectra, while already the second Born, which is the simplest time-nonlocal approximation, reproduces well most of the additional excitations, which are characterized as double-excitations.