  We study an XXZ spin chain, where each spin is coupled to an independent
ohmic bath of harmonic oscillators at zero temperature. Using bosonization and
numerical techniques, we show the existence of two phases separated by an
Kosterlitz-Thouless (KT) transition. At low coupling with the bath, the chain
remains in a Luttinger liquid phase with a reduced but finite spin stiffness,
while above a critical coupling the system is in a dissipative phase
characterized by a vanishing spin stiffness. We argue that the transport
properties are also inhibited: the Luttinger liquid is a perfect conductor
while the dissipative phase displays finite resistivity. Our results show that
the effect of the bath can be interpreted as annealed disorder inducing
signatures of localization.
