Abstract
Interactions in quantum systems may induce transitions to exotic correlated phases of matter which can be vulnerable to coupling to an environment. Here, we study the stability of a Bose-Hubbard chain coupled to a bosonic bath at zero and nonzero temperature. We show that only above a critical interaction the chain loses bosons and its properties are significantly affected. The transition is of a different nature than the superfluid-Mott-insulator transition and occurs at a different critical interaction. We explain such a stable-unstable transition by the opening of a global charge gap. The comparison of accurate matrix product state simulations to approximative approaches that miss this transition reveals its many-body origin.