Density-functional theory for the Dicke Hamiltonian
Abstract
A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a Hohenberg-Kohn theorem that manifests the magnetization and displacement as internal variables, along with several representability results. The constrained-search functionals for pure states and ensembles are introduced and analyzed. We find the optimizers for the pure-state constrained-search functional to be low-lying eigenstates of the Hamiltonian and, based on the properties of the optimizers, we formulate an adiabatic-connection formula. In the reduced case of the Rabi model we can even show differentiability of the universal density functional, which amounts to unique pure-state v-representability.
Cite
@article{arxiv.2409.13767,
title = {Density-functional theory for the Dicke Hamiltonian},
author = {Vebjørn H. Bakkestuen and Mihály A. Csirik and Andre Laestadius and Markus Penz},
journal= {arXiv preprint arXiv:2409.13767},
year = {2025}
}