No-Go Theorem for Quasiparticle BEC in the Spin-Boson Model

TL;DR

This paper proves a no-go theorem showing that Bose-Einstein condensation does not occur for quasiparticles in the spin-boson model at finite temperature, despite formal similarities to free Bose gases.

Contribution

It provides a rigorous theoretical proof excluding BEC of quasiparticles in the spin-boson model, extending understanding of quantum phase transitions.

Findings

Quasiparticles in the spin-boson model do not undergo BEC at finite temperature.

Formal similarities to free Bose gases do not imply actual BEC in this model.

A no-go theorem is established for moderate equilibrium states.

Abstract

We analyze the possibility of Bose-Einstein condensation (BEC) at finite temperature in the spin-boson model within the frameworks of functional integral representations and the resolvent algebra. Because a sesquilinear form arising from the zero mode appears, analogous to the case of the free Bose gas, a BEC-type component is also formally present in the spin-boson model. However, according to arxiv:1207.4621, quasiparticles do not undergo BEC, so an argument is needed to exclude this possibility. In particular, for moderate equilibrium states defined by following the formulation of that paper, a no-go theorem for BEC is obtained.