Asymptotics in Spin-Boson type models

TL;DR

This paper analyzes the asymptotic behavior of Spin-Boson models with a qubit interacting with a bosonic field, revealing limitations of renormalization schemes and the existence of excited states at large interaction strengths.

Contribution

It establishes the asymptotic limits of the Hamiltonian in strong coupling regimes and demonstrates the existence of excited states in massive Spin-Boson models.

Findings

Renormalization schemes become independent of the qubit at strong coupling.

Excited states exist for large interaction strengths.

Asymptotic limits of physical quantities are computed.

Abstract

In this paper we investigate a family of models for a qubit interacting with a bosonic field. More precisely, we find asymptotic limits of the Hamiltonian as the strength of the interaction tends to infinity. The main result has two applications. First of all, we show that self-energy renormalisation schemes similar to that of the Nelson model will never give a physically interesting result. This is because any limit obtained through such a scheme would be independent of the qubit. Secondly, we find that exited states exist in the massive Spin-Boson models for sufficiently large interaction strengths. We are also able to compute the asymptotic limit of many physical quantities.