On Asymptotic Expansions in Spin Boson Models

TL;DR

This paper proves the existence of arbitrary order asymptotic expansions for ground states and energies in generalized spin boson models, under mild infrared assumptions, extending previous analyticity results.

Contribution

It establishes the existence of asymptotic expansions in spin boson models under weaker infrared conditions than traditional methods.

Findings

Asymptotic expansions exist to arbitrary order for ground states and energies.

The results hold under a natural, mild infrared assumption.

Complemented previous analyticity properties in the models.

Abstract

We consider expansions of eigenvalues and eigenvectors of models of quantum field theory. For a class of models known as generalized spin boson model we prove the existence of asymptotic expansions of the ground state and the ground state energy to arbitrary order. We need a mild but very natural infrared assumption, which is weaker than the assumption usually needed for other methods such as operator theoretic renormalization to be applicable. The result complements previously shown analyticity properties.