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Spin-boson type models analyzed using symmetries

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We analyze a family of models for a qubit interacting with a bosonic field. This family of models is very large and contains models where higher-order perturbations of field operators are added to the Hamiltonian. The Hamiltonian has a special symmetry, called spin-parity symmetry, which plays a central role in our analysis. Using this symmetry, we find the domain of self-adjointness and we decompose the Hamiltonian into two fiber operators each defined on Fock space. We then prove the Hunziker-van Winter-Zhislin (HVZ) theorem for the fiber operators, and we single out a particular fiber operator which has a ground state if and only if the full Hamiltonian has a ground state. From these results, we deduce a simple criterion for the existence of an excited state.

OriginalsprogEngelsk
TidsskriftKyoto Journal of Mathematics
Vol/bind60
Nummer4
Sider (fra-til)1261-1332
Antal sider72
ISSN2156-2261
DOI
StatusUdgivet - dec. 2020

Bibliografisk note

Funding Information:
Acknowledgments. Dam’s work was partially supported by the Independent Research Fund Denmark through the project “Mathematics of Dressed Particles.”

Publisher Copyright:
© 2020 by Kyoto University

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

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