Ground States in the Spin Boson Model

TL;DR

This paper proves the existence, uniqueness, and analyticity of the ground state in the spin-boson model without infrared regularization, using a modified renormalization approach and perturbation theory.

Contribution

It establishes the ground state properties of the spin-boson model for small coupling constants without infrared regularization, advancing theoretical understanding.

Findings

Ground state exists for small coupling lambda

Ground state energy is analytic in lambda

Ground state is unique and can be computed via perturbation theory

Abstract

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 small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory.