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

@inproceedings{Hinrichs2022ExistenceOG, title={Existence of Ground States in the Infrared-Critial Spin Boson Model}, author={Benjamin Hinrichs}, year={2022} }

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 λc > 0 such that the spin boson model exhibits a ground state for coupling constants λ with |λ| < λc. 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…

## References

SHOWING 1-10 OF 25 REFERENCES

### Ground States in the Spin Boson Model

- Physics, Mathematics
- 2011

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for…

### The Ground State Energy of the Massless Spin-Boson Model

- Physics
- 2010

We provide an explicit combinatorial expansion for the ground state energy of the massless spin-Boson model as a power series in the coupling parameter. Our method uses the technique of cluster…

### Ground state(s) of the spin-boson hamiltonian

- Physics
- 1989

We establish that the finite temperature KMS states of the spin-boson hamiltonian have a limit as the temperature drops to zero. Using recent advances on the one-dimensional Ising model with long…

### FKN Formula and Ground State Energy for the Spin Boson Model with External Magnetic Field

- Physics, MathematicsAnnales Henri Poincaré
- 2022

We consider the spin boson model with external magnetic field. We prove a path integral formula for the heat kernel, known as Feynman–Kac–Nelson (FKN) formula. We use this path integral…

### On Existence of Ground States in the Spin Boson Model

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2021

We show the existence of ground states in the massless spin boson model without any infrared regularization. Our proof is non-perturbative and relies on a compactness argument. It works for arbitrary…

### Spin-boson type models analyzed using symmetries

- Mathematics
- 2018

In this paper we analyse a family of models for a qubit interacting with a bosonic field. These models have a parity symmetry, which enables them to have a ground state even in some infrared…

### On the absence of eigenvectors of Hamiltonians in a class of massless quantum field models without infrared cutoff

- Physics
- 1998

A class of models of quantized, massless Bose fields, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal.151 (1997), 455–503) is considered. Theorems on the absence of…

### The Infrared Behaviour in Nelson's Model of a Quantum Particle Coupled to a Massless Scalar Field

- Physics
- 2000

Abstract. We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian has no ground state in Fock space and thus it is not…