Dissipative Frustration in a One Dimensional Josephson Junction Chain

We study the influence of dissipative frustration on the one dimensional Josephson junction chain. In particular we analyze the dissipative quantum phase transition between the chain being superconducting or insulating, the purity as a measure of quantum--environment correlation and the logarithmic negativity as an entanglement measure. The dissipative frustration is provided by coupling two non-commuting operators to the environment. A possible realization of these environmental couplings are shunt resistances between the superconducting islands and resistances to the ground. Using a self-consistent harmonic approximation we determine the critical line separating superconducting and insulating phases and find a nonmonotonic behavior as a function of the dissipative strength. The interplay between both environmental couplings is also reflected in the purity and the logarithmic negativity. We find a change in their behavior depending whether a second bath is present or not.