Calculating excitation energies with the help of cumulants

TL;DR

This paper extends the cumulant-based approach from ground-state energies to excited states in quantum many-body systems, enabling size-consistent approximations and application to semiconductor energy bands.

Contribution

It introduces a method to express excited state energies using cumulants, enhancing approximation schemes and size consistency in quantum energy calculations.

Findings

Expressed excited state energies via cumulants

Applied method to semiconductor energy bands

Re-derived known results with simplified models

Abstract

Recently, it has been shown that the ground-state energy of a quantum many-body system can be written in terms of cumulants. In this paper we show that the energies of excited states can be expressed similarly. These representations are suitable for various approximation schemes, e.g., projection techniques. The explicit use of cumulants ensures size consistency in all approximations. The theory is then applied to the computation of the energy bands of a semiconductor with diamond structure. As we focus especially on the effects of electron correlations, we consider a simplified model and re-derive results obtained previously by the variational Local Ansatz method.