Localization induced by spatially uncorrelated subohmic baths in one dimension

We study an incommensurate XXZ spin chain coupled to a collection of local harmonic baths. At zero temperature, by varying the strength of the coupling to the bath the chain undergoes a quantum phase transition between a Luttinger liquid phase and a spin-density wave (SDW). Our results are consistent with the Berezinskii-Kosterlitz-Thouless (BKT) transition. As opposed to the standard mechanism, the SDW emerges in the absence of the opening of a gap, but it is due to "fractional excitations" induced by the bath. We also show, by computing the DC conductivity, that the system is insulating in the presence of a subohmic bath. We interpret this phenomenon as localization induced by the bath a la Caldeira and Leggett.