Effects of dissipation on quantum phase transitions - art. no. 125322

We discuss the effect of dissipation on quantum phase transitions. In parti cular, we concentrate on the superconductor to insulator and quantum Hall t o insulator transitions. By invoicing a phenomenological parameter alpha to describe the coupling of the system to a continuum of degrees of freedom r epresenting the dissipative bath, we obtain phase diagrams for the quantum Hall and superconductor-insulator problems. Our main result is that, in two dimensions, the metallic phases observed in finite magnetic fields (possib ly also strictly zero field) are adiabatically deformable from one to the o ther. This is plausible, as there is no broken symmetry that differentiates them.