The Ground State Energy of The Massless Spin-Boson Model

TL;DR

This paper derives an explicit power series expansion for the ground state energy of the massless spin-Boson model using cluster expansion, providing convergence bounds without renormalization techniques.

Contribution

It introduces a combinatorial expansion method for the model's ground state energy, avoiding multiscale and renormalization group analysis, and establishes its analyticity.

Findings

Explicit power series expansion for ground state energy

Proven analyticity and convergence bounds

Connection to loop-erased random walk

Abstract

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 expansion in constructive quantum field theory and takes as a starting point the functional integral representation and its reduction to an Ising model on the real line with long range interactions. We prove the analyticity of our expansion and provide an explicit lower bound on the radius of convergence. We do not need multiscale nor renormalization group analysis. A connection to the loop-erased random walk is indicated.