Dissipation-induced first-order decoherence phase transition in a noninteracting fermionic system

Abstract

We consider a quantum wire connected to the leads and subjected to dissipation along its length. The dissipation manifests as tunneling into (out of) the chain from (to) a memoryless environment. The evolution of the system is described by the Lindblad equation. Already infinitesimally small dissipation along the chain induces a quantum phase transition (QPT). This is a decoherence QPT: the reduced density matrix of a subsystem in the nonequilibrium steady state (far from the ends of the chain) can be represented as the tensor product of single-site density matrices. The QPT is identified from the jump of the current and the entropy per site as the dissipation becomes nonzero. We also explore the properties of the boundaries of the chain close to the transition point and observe that the boundaries behave as if they undergo a second-order phase transition as a function of the dissipation strength: the particle-particle correlation functions and the response to the electric field exhibit a power-law divergence. Disorder is known to localize one-dimensional systems, but the coupling to the memoryless environment pushes the system back into the delocalized state even in the presence of disorder. Interestingly, we observe a similar transition in the classical dissipative counterflow model: the current has a jump at the ends of the chain introducing an infinitely small dissipation.