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

TL;DR

This paper reviews recent findings on the existence of ground states in the infrared-critical spin boson model, identifying a critical coupling below which ground states exist, using a combination of probabilistic and correlation techniques.

Contribution

It establishes the existence of a critical coupling for ground states in the infrared-critical spin boson model and combines multiple analytical methods for the proof.

Findings

Existence of a critical coupling constant $\lambda_c$ for ground states.

Ground states exist for coupling constants with $|\lambda|<\lambda_c$.

Conjecture that no ground state exists at large coupling.

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.