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

@article{Sekine2013PhononBC, title={Phonon Bose-Einstein condensation in a Hubbard-phonon interacting system with infrared divergence}, author={Yoshitsugu Sekine}, journal={arXiv: Mathematical Physics}, year={2013} }

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.

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