Quantum-electrodynamical density-functional theory for the Dicke Hamiltonian

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...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Bakkestuen, Vebjørn H, Csirik, Mihály A, Laestadius, Andre, Penz, Markus
Format: Article
Language:English
Subjects:
Constraints
Density functional theory
Eigenvectors
Hamiltonian functions
Magnetic properties
Online Access:Get full text
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Summary: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.
ISSN:2331-8422