Entanglement transitions in a boundary-driven open quantum many-body system

Abstract: We present a numerical framework based on tree tensor operators that enables large-scale simulation of out-of-equilibrium open quantum many-body systems. By design, it protects density operator positivity and provides direct access to entanglement monotones, such as entanglement of formation and logarithmic negativity. To demonstrate the framework's ability to probe entanglement in open quantum many-body systems and distinguish it from other correlations, we study a paradigmatic open system problem: the boundary-driven XXZ spin-chain. We uncover entanglement transitions driven by both the coupling to the environment and the anisotropy parameter. These transitions reveal an immediate connection between entanglement and spin-current, and link the known transport regimes of the model to distinct entanglement regimes, i.e., separable, area-law, and volume-law. Our work enables the analysis of entanglement in open quantum many-body systems out of equilibrium, a necessary step for developing scalable quantum technologies.