A stable, critical phase induced by Berry phase and dissipation in a spin-chain*

Motivated from experiments on spin-chains embedded in a metallic bath, as well as closed quantum systems described by long-range interacting Hamiltonians, we study a critical SU(N) spin-chain perturbed by dissipation, or equivalently, after space-time rotation, long-range spatial interactions. The interplay of dissipation and the Wess-Zumino (Berry phase) term results in a rich phase diagram with multiple fixed points of renormalization group. For a range of the exponent that characterizes the dissipative bath, we find a second-order phase transition between the CFT fixed point which describes an isolated chain, and a dissipation-induced-ordered phase. More interestingly, for a different range of the exponent, we find a stable, gapless, non-relativistic phase of matter whose existence necessarily requires coupling to the dissipative bath. Upon tuning the exponent, we find that the fixed-point corresponding to this gapless, stable phase 'annihilates' the fixed point that describes the transition out of this phase to the ordered phase. We also study a relativistic version of our model, and identify a new critical point. We discuss implications of our work for Kondo lattice systems, and engineered long-range interacting quantum systems.