Phonon Bose-Einstein condensation in a Hubbard-phonon interacting system with infrared divergence

TL;DR

This paper demonstrates that a Hubbard-phonon system can exhibit phonon Bose-Einstein condensation and gauge symmetry breaking at low temperatures, using advanced mathematical tools like unitary transformations and the Araki-Woods representation.

Contribution

It establishes the occurrence of phonon BEC and gauge symmetry breaking in a Hubbard-phonon system, extending understanding of quantum phase transitions in such models.

Findings

Phonon BEC occurs at low temperatures in the system.

Gauge symmetry breaking for phonons is demonstrated.

The system behaves similarly to a free or van Hove model.

Abstract

We show that a finite Hubbard-phonon interacting system exhibits phonon BEC at sufficiently low temperature. We also have the gauge symmetry breaking for phonons. The key tools are a unitary transformation introduced by Arai and Hirokawa \protect{\cite{AH1}} and the Araki-Woods representation. This system is essentially the same as a free system or the van Hove model.