conference paper published Benjamin Hinrichs author 994270000-0001-9074-1205 FumioHiroshima editor Mathematical aspects of quantum fields and related topics 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. 2022RIMS, Kyoto eng 2204.00287 223560-73 yes B. Hinrichs, “Existence of Ground States in the Infrared-Critial Spin Boson Model,” in <i>Mathematical aspects of quantum fields and related topics</i>, RIMS, Kyoto, 2022, vol. 2235, pp. 60–73. Hinrichs, B. (2022). Existence of Ground States in the Infrared-Critial Spin Boson Model. In F. Hiroshima (Ed.), <i>Mathematical aspects of quantum fields and related topics</i> (Vol. 2235, pp. 60–73). Hinrichs, Benjamin. “Existence of Ground States in the Infrared-Critial Spin Boson Model.” In <i>Mathematical Aspects of Quantum Fields and Related Topics</i>, edited by Fumio Hiroshima, 2235:60–73. RIMS Kôkyûroku, 2022. B. Hinrichs, in: F. Hiroshima (Ed.), Mathematical Aspects of Quantum Fields and Related Topics, 2022, pp. 60–73. Hinrichs, Benjamin. “Existence of Ground States in the Infrared-Critial Spin Boson Model.” <i>Mathematical Aspects of Quantum Fields and Related Topics</i>, edited by Fumio Hiroshima, vol. 2235, 2022, pp. 60–73. @inproceedings{Hinrichs_2022, series={RIMS Kôkyûroku}, title={Existence of Ground States in the Infrared-Critial Spin Boson Model}, volume={2235}, booktitle={Mathematical aspects of quantum fields and related topics}, author={Hinrichs, Benjamin}, editor={Hiroshima, Fumio}, year={2022}, pages={60–73}, collection={RIMS Kôkyûroku} } Hinrichs B. Existence of Ground States in the Infrared-Critial Spin Boson Model. In: Hiroshima F, ed. <i>Mathematical Aspects of Quantum Fields and Related Topics</i>. Vol 2235. RIMS Kôkyûroku. ; 2022:60-73. 434962023-04-14T04:56:51Z2026-01-16T09:03:41Z