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arXiv · 2204.00287

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

Benjamin Hinrichs
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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.

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Benjamin Hinrichs. 2022-04-01. Existence of Ground States in the Infrared-Critial Spin Boson Model. https://arxiv.org/abs/2204.00287

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