Quantum phase transitions of a Bose-Einstein condensate

Abstract

Bose-Einstein condensates display quantum phase transitions that cannot be explained with a mean field theory. Describing each trap as an effective site of a Bose-Hubbard model and using the Schwinger representation the system can be mapped onto spin models. We show that it is possible to define correlations between bosons in such a way that critical behaviour is associated to the divergence of a correlation length accompanied by a gapless spectrum in the thermodynamic limit. Such description provides critical exponents and encompasses the notion of universality.