Laboratoire de Physique Théorique
Toulouse - UMR 5152

A system that undergoes continuous phase transitions may exhibit a phase with coexistence of two orders, which implies the spontaneous breaking of two kinds of symmetry. We analyzed a fully connected model and found that this model exhibits three low temperature phases separated by continuous phase transitions : an insulating, glassy phase with an amorphous frozen density pattern, a non-glassy superfluid phase and an intermediate phase, in which both types of order coexist. Further, we investigated the properties of the coexistence ("superglass") phase. We found anticorrelations between the local order parameters and a non-monotonous superfluid order parameter as a function of T. It is natural to extend this fully connected model to a Bethe lattice with finite but large connectivity. The thermodynamic properties will not change so much in the Bethe lattice case, but the quantum fluctuations will play a very important role for the dynamics in the glassy insulator. By using the cavity-mean field method developed by Ioffe and Mezard we found that the SI transition is suppressed by the pseudo gap in the density of states of the glass state. We found that, the glassy insulator has a finite mobility edge for the bosonic excitations, which does not close upon approaching the quantum critical point.