Spin-boson type models analyzed using symmetries

Thomas Norman Dam; Jacob Schach Møller

doi:10.1215/21562261-2019-0062

Spin-boson type models analyzed using symmetries

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

3 Citationer (Scopus)

Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Kyoto Journal of Mathematics
Vol/bind	60
Nummer	4
Sider (fra-til)	1261-1332
Antal sider	72
ISSN	2156-2261
DOI	https://doi.org/10.1215/21562261-2019-0062
Status	Udgivet - dec. 2020

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10.1215/21562261-2019-0062

https://arxiv.org/pdf/1803.05812v3.pdf

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AB - 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.

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Spin-boson type models analyzed using symmetries

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