Spin-boson type models analyzed using symmetries

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.