Density-functional theory for the Dicke Hamiltonian

• URL: http://arxiv.org/abs/2409.13767v2
• Date: Wed, 23 Apr 2025 07:14:15 GMT
• Title: Density-functional theory for the Dicke Hamiltonian
• Authors: Vebjørn H. Bakkestuen, Mihály A. Csirik, Andre Laestadius, Markus Penz,
• Abstract summary: A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided.<n>In particular, the quantum Rabi model, the Dicke model, and the latter to multiple modes are considered.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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