Second order quantum phase transition of a homogeneous Bose gas with   attractive interactions
  We consider a homogeneous Bose gas of particles with an attractive interaction. Mean field theory predicts for this system a spontaneous symmetry breaking at a certain value of the interaction strength. We show that at this point a second-order quantum phase transition occurs. We investigate the system in the vicinity of the critical point using Bogoliubov theory and a continuous description, that allows us to analyze {\it quantum fluctuations} in the system even when the Bogoliubov approach breaks down. 
P. Zi\'n, B. Ole\'s, M. Trippenbach, and K. Sacha