The dissipation induced by a metallic gate on the low-energy properties of interacting 1D electron liquids is studied. As a function of the distance to the gate, or the electron density in the wire, the system can undergo a quantum phase transition from a Tomonaga-Luttinger liquid to two kinds of dissipative phases, one of them with a finite spatial correlation length. We also define a dual model, which describes an attractive one-dimensional metal with a Josephson coupling to a dirty metallic lead.

• Received 8 March 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.076401