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