Density-functional theory for the Dicke Hamiltonian
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913804921602048 |
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| author | Bakkestuen, Vebjørn H. Csirik, Mihály A. Laestadius, Andre Penz, Markus |
| author_facet | Bakkestuen, Vebjørn H. Csirik, Mihály A. Laestadius, Andre Penz, Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density-functional theory for the Dicke Hamiltonian Bakkestuen, Vebjørn H. Csirik, Mihály A. Laestadius, Andre Penz, Markus Mathematical Physics Quantum Physics 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. |
| title | Density-functional theory for the Dicke Hamiltonian |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2409.13767 |