Dissipative phase transition with quantum frustration

We study the quantum phase transition of the one dimensional phase model in presence of quantum frustration, provided by a dissipative interaction of the system with the environment through two non-commuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between a long-range ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with charge localization. We find that the critical line separating the two phases has a nonmonotonic behavior as a function of the dissipative coupling strength. Moreover, we analyse the purity of the system that quantifies the degree of correlation between the system and the environment, and the logarithmic negativity as entanglement measure that encodes the internal quantum correlations in the system.