Dissipative effects on quantum glassy systems

We discuss the behavior of a quantum glassy system coupled to a bath of quantum oscillators. We show that the system localizes in the absence of interactions when coupled to a sub-Ohmic bath. When interactions are switched on localization disappears and the system undergoes a phase transition towards a glassy phase. We show that the position of the critical line separating the disordered and ordered phases strongly depends on the coupling to the bath. For a given type of bath, the ordered glassy phase is favored by a stronger coupling. Ohmic, sub-Ohmic, and super-Ohmic baths lead to different transition lines. We draw our conclusions from analysis of the partition function using the replicated imaginary-time formalism and from the study of the real-time dynamics of the coupled system using the Schwinger-Keldysh closed time-path formalism.