Spin-Boson Model

pFumio Hiroshimap

Kurt Fischer

We introduce a boson-impurity model, and prove that it is in the same universality class as the one-dimensional Ising model with algebraic decaying interaction. This boson-impurity model can be derived from the spin-boson model. The spin-boson model itself is therefore in the same universality class as well. Because the boson-impurity model contains only virtual spin-fluctuations, these are already enough to drive the quantum phase transition of the sub-ohmic spin-boson model.

Abraham Klein

Luigi Accardi, Igor Vasil'evich Volovich, Yun Gang Lu

Hinrichs, Benjamin

We review recent results on the existence of ground states for the infrared-critical spin boson model, which describes the interaction of a massless bosonic field with a two-state quantum system. Explicitly, we derive a critical coupling $λ_{\mathsf c}>0$ such that the spin boson model exhibits a ground state for coupling constants $λ$ with $|λ|<λ_{\mathsf c}$. The proof combines a Feynman-Kac-Nelson formula for the spin boson model with external magnetic field, a 1D-Ising model correlation bound and a compactness argument in Fock space. Elaborating on the connection to a long-range 1D-Ising model, we briefly discuss the conjecture that the spin boson model does not have a ground state at large coupling. This note is based on joint work with David Hasler and Oliver Siebert.

Yoshitsugu Sekine

We analyze the possibility of Bose-Einstein condensation (BEC) at finite temperature in the spin-boson model within the frameworks of functional integral representations and the resolvent algebra. Because a sesquilinear form arising from the zero mode appears, analogous to the case of the free Bose gas, a BEC-type component is also formally present in the spin-boson model. However, according to arxiv:1207.4621, quasiparticles do not undergo BEC, so we have to exclude this possibility. A no-go theorem for BEC is obtained, but we find that the spin-boson model is not a model that follows the criterion in arxiv:1207.4621.