Existence of Ground States in the Infrared-Critial Spin Boson Model

Abstract

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 ${\lambda }_{\mathsf{c}}>0$ such that the spin boson model exhibits a ground state for coupling constants $\lambda$ with $|\lambda |<{\lambda }_{\mathsf{c}}$. 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.

arXiv comment13 pages, contribution to the proceedings of the 2021 RIMS Workshop 'Mathematical Aspects of Quantum Fields and Related Topics'