  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 non-zero 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 charge gap. The comparison of
accurate matrix product state simulations to approximative approaches that miss
this transition reveals its many-body origin.
